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<div class="js-react-on-rails-component" style="display:none" data-component-name="ProfileCheckPaperUpdate" data-props="{}" data-trace="false" data-dom-id="ProfileCheckPaperUpdate-react-component-71d35f58-e3de-4c64-a800-0d4423d61ed8"></div> <div id="ProfileCheckPaperUpdate-react-component-71d35f58-e3de-4c64-a800-0d4423d61ed8"></div> <div class="DesignSystem"><div class="onsite-ping" id="onsite-ping"></div></div><div class="profile-user-info DesignSystem"><div class="social-profile-container"><div class="left-panel-container"><div class="user-info-component-wrapper"><div class="user-summary-cta-container"><div class="user-summary-container"><div class="social-profile-avatar-container"><img class="profile-avatar u-positionAbsolute" alt="Sam Buss" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" 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style="margin: 0px;"><b>Address: </b>La Jolla, California, United States<br /><div class="js-profile-less-about u-linkUnstyled u-tcGrayDarker u-textDecorationUnderline u-displayNone">less</div></div></div><div class="ri-section"><div class="ri-section-header"><span>Interests</span></div><div class="ri-tags-container"><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="5937540" href="https://www.academia.edu/Documents/in/Mathematics"><div id="js-react-on-rails-context" style="display:none" data-rails-context="{"inMailer":false,"i18nLocale":"en","i18nDefaultLocale":"en","href":"https://ucsd.academia.edu/SamBuss","location":"/SamBuss","scheme":"https","host":"ucsd.academia.edu","port":null,"pathname":"/SamBuss","search":null,"httpAcceptLanguage":null,"serverSide":false}"></div> <div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Mathematics"]}" data-trace="false" data-dom-id="Pill-react-component-482ab391-ae21-40ce-ad29-9b39edf9ecc2"></div> <div id="Pill-react-component-482ab391-ae21-40ce-ad29-9b39edf9ecc2"></div> </a><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="5937540" href="https://www.academia.edu/Documents/in/Computer_Science"><div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Computer Science"]}" data-trace="false" data-dom-id="Pill-react-component-8b8a1fc3-95fa-4125-bdfa-8076692ac1c0"></div> <div id="Pill-react-component-8b8a1fc3-95fa-4125-bdfa-8076692ac1c0"></div> </a><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="5937540" href="https://www.academia.edu/Documents/in/Music"><div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Music"]}" data-trace="false" data-dom-id="Pill-react-component-32f68b33-6a4d-4e6c-956f-31d994bc68cf"></div> <div id="Pill-react-component-32f68b33-6a4d-4e6c-956f-31d994bc68cf"></div> </a><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="5937540" href="https://www.academia.edu/Documents/in/Statistics"><div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Statistics"]}" data-trace="false" data-dom-id="Pill-react-component-dbb4da0c-351e-4a2a-81c9-f9382dac67e3"></div> <div id="Pill-react-component-dbb4da0c-351e-4a2a-81c9-f9382dac67e3"></div> </a><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="5937540" href="https://www.academia.edu/Documents/in/Mathematics_Education"><div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Mathematics Education"]}" data-trace="false" data-dom-id="Pill-react-component-8b21484d-f7bd-4e50-80ee-bd54060e0ca0"></div> <div id="Pill-react-component-8b21484d-f7bd-4e50-80ee-bd54060e0ca0"></div> </a></div></div><div class="external-links-container"><ul class="profile-links new-profile js-UserInfo-social"><li class="profile-profiles js-social-profiles-container"><i class="fa fa-spin fa-spinner"></i></li></ul></div></div></div><div class="right-panel-container"><div class="user-content-wrapper"><div class="uploads-container" id="social-redesign-work-container"><div class="upload-header"><h2 class="ds2-5-heading-sans-serif-xs">Uploads</h2></div><div class="documents-container backbone-social-profile-documents" style="width: 100%;"><div class="u-taCenter"></div><div class="profile--tab_content_container js-tab-pane tab-pane active" id="all"><div class="profile--tab_heading_container js-section-heading" data-section="Papers" id="Papers"><h3 class="profile--tab_heading_container">Papers by Sam Buss</h3></div><div class="js-work-strip profile--work_container" data-work-id="21480120"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/21480120/Cobham_recursive_set_functions"><img alt="Research paper thumbnail of Cobham recursive set functions" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480120/Cobham_recursive_set_functions">Cobham recursive set functions</a></div><div class="wp-workCard_item"><span>Annals of Pure and Applied Logic</span><span>, 2016</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action 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profile--work_container" data-work-id="21480119"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/21480119/Cut_Elimination_In_Situ"><img alt="Research paper thumbnail of Cut Elimination In Situ" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480119/Cut_Elimination_In_Situ">Cut Elimination In Situ</a></div><div class="wp-workCard_item"><span>Gentzen's Centenary</span><span>, 2015</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT We present methods for removing top-level cuts from a sequent calculus or Tait-style pro...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT We present methods for removing top-level cuts from a sequent calculus or Tait-style proof without significantly increasing the space used for storing the proof. For propositional logic, this requires con-verting a proof from tree-like to dag-like form, but it most doubles the number of lines in the proof. For first-order logic, the proof size can grow exponentially, but the proof has a succinct description and is polynomial-time uniform. We use direct, global constructions that give polynomial time methods for removing all top-level cuts from proofs. By exploiting prenex representations, this extends to removing all cuts, with final proof size bounded superexponentially in the alternation of quantifiers in cut formulas.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480119"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480119"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480119; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=21480119]").text(description); $(".js-view-count[data-work-id=21480119]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 21480119; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='21480119']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 21480119, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=21480119]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":21480119,"title":"Cut Elimination In Situ","translated_title":"","metadata":{"abstract":"ABSTRACT We present methods for removing top-level cuts from a sequent calculus or Tait-style proof without significantly increasing the space used for storing the proof. 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This is an extension of earlier work on t h e classical Bounded Arithmetic and was first conjectured by S. Cook. In contrast t o t h e classical theories of Bounded b Arithmetic where Ci-definable functions are of interest, our results for intuitionistic theories concern all the definable functions. The method of proof uses 0;-realizability which is inspired by t h e recursive realizability of S.C. Kleene 131 and D. Nelson 151. I t also involves polynomial hierarchy functionals of finite type which a r e introduced in this paper. * Research supported in part by NSF Grant DMS 85-11465. In general, 0: is P The theories Si a r e most advantageously viewed a s Gentzen-style natural deduction systems. A formal proof in a natural deduction system contains sequents of t h e form where each A. and B. is a formula. The meaning of such a sequent is J J In addition t o t h e usual inference rules for natural deduction. the Z:-PIND inference is b</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="bff228b6fcf217bc140bb172bfcba6e8" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41904058,"asset_id":21480116,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41904058/download_file?st=MTczNDU0MTQ1OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480116"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480116"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480116; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=21480116]").text(description); $(".js-view-count[data-work-id=21480116]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 21480116; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='21480116']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 21480116, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "bff228b6fcf217bc140bb172bfcba6e8" } } $('.js-work-strip[data-work-id=21480116]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":21480116,"title":"The polynomial hierarchy and intuitionistic Bounded Arithmetic","translated_title":"","metadata":{"grobid_abstract":"Intuitionistic theories IS: of Bounded Arithmetic a r e introduced and i t is shown t h a t the definable functions of IS: a r e precisely the 0: functions of t h e polvnomial hierarchy. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="21480113"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/21480113/The_Computational_Power_of_Bounded_Arithmetic_from_the_Predicative_Viewpoint"><img alt="Research paper thumbnail of The Computational Power of Bounded Arithmetic from the Predicative Viewpoint" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480113/The_Computational_Power_of_Bounded_Arithmetic_from_the_Predicative_Viewpoint">The Computational Power of Bounded Arithmetic from the Predicative Viewpoint</a></div><div class="wp-workCard_item"><span>New Computational Paradigms</span><span>, 2008</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT This paper considers theories of bounded arithmetic that are predicative in the sense of...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT This paper considers theories of bounded arithmetic that are predicative in the sense of Nelson, that is, theories that are interpretable in Robinson’s Q.We give a nearly exact characterization of functions that can be total in predicative bounded theories. As an upper bound, any such function has a polynomial growth rate and its bit-graph is in nondeterministic exponential time and in co-nondeterministic exponential time. In fact, any function uniquely defined in a bounded theory of arithmetic lies in this class. Conversely, any function that is in this class (provably in IΔ0+exp) can be uniquely defined and total in a (predicative) bounded theory of arithmetic.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480113"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480113"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480113; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=21480113]").text(description); $(".js-view-count[data-work-id=21480113]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 21480113; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='21480113']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 21480113, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=21480113]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":21480113,"title":"The Computational Power of Bounded Arithmetic from the Predicative Viewpoint","translated_title":"","metadata":{"abstract":"ABSTRACT This paper considers theories of bounded arithmetic that are predicative in the sense of Nelson, that is, theories that are interpretable in Robinson’s Q.We give a nearly exact characterization of functions that can be total in predicative bounded theories. As an upper bound, any such function has a polynomial growth rate and its bit-graph is in nondeterministic exponential time and in co-nondeterministic exponential time. In fact, any function uniquely defined in a bounded theory of arithmetic lies in this class. Conversely, any function that is in this class (provably in IΔ0+exp) can be uniquely defined and total in a (predicative) bounded theory of arithmetic.","publication_date":{"day":null,"month":null,"year":2008,"errors":{}},"publication_name":"New Computational Paradigms"},"translated_abstract":"ABSTRACT This paper considers theories of bounded arithmetic that are predicative in the sense of Nelson, that is, theories that are interpretable in Robinson’s Q.We give a nearly exact characterization of functions that can be total in predicative bounded theories. As an upper bound, any such function has a polynomial growth rate and its bit-graph is in nondeterministic exponential time and in co-nondeterministic exponential time. In fact, any function uniquely defined in a bounded theory of arithmetic lies in this class. Conversely, any function that is in this class (provably in IΔ0+exp) can be uniquely defined and total in a (predicative) bounded theory of arithmetic.","internal_url":"https://www.academia.edu/21480113/The_Computational_Power_of_Bounded_Arithmetic_from_the_Predicative_Viewpoint","translated_internal_url":"","created_at":"2016-02-02T14:51:45.108-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":5937540,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"The_Computational_Power_of_Bounded_Arithmetic_from_the_Predicative_Viewpoint","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":"ABSTRACT This paper considers theories of bounded arithmetic that are predicative in the sense of Nelson, that is, theories that are interpretable in Robinson’s Q.We give a nearly exact characterization of functions that can be total in predicative bounded theories. As an upper bound, any such function has a polynomial growth rate and its bit-graph is in nondeterministic exponential time and in co-nondeterministic exponential time. In fact, any function uniquely defined in a bounded theory of arithmetic lies in this class. Conversely, any function that is in this class (provably in IΔ0+exp) can be uniquely defined and total in a (predicative) bounded theory of arithmetic.","owner":{"id":5937540,"first_name":"Sam","middle_initials":null,"last_name":"Buss","page_name":"SamBuss","domain_name":"ucsd","created_at":"2013-10-04T05:16:03.538-07:00","display_name":"Sam Buss","url":"https://ucsd.academia.edu/SamBuss"},"attachments":[],"research_interests":[],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="21480112"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/21480112/On_Model_Theory_for_Intuitionistic_Bounded_Arithmetic_with_Applications_to_Independence_Results"><img alt="Research paper thumbnail of On Model Theory for Intuitionistic Bounded Arithmetic with Applications to Independence Results" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480112/On_Model_Theory_for_Intuitionistic_Bounded_Arithmetic_with_Applications_to_Independence_Results">On Model Theory for Intuitionistic Bounded Arithmetic with Applications to Independence Results</a></div><div class="wp-workCard_item"><span>Feasible Mathematics</span><span>, 1990</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">... It is open whether the theory CPV= S\(PV) can prove NPB ... Mi^ M} if and only if i i&lt; j. ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">... It is open whether the theory CPV= S\(PV) can prove NPB ... Mi^ M} if and only if i i&lt; j. 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Rather than considering the usual fragments defined by the amount of induction they allow, we study Jeřábek&amp;#39;s theories for approximate counting and their subtheories. We show that the ∀Σ b 1 Herbrandized ordering principle is unprovable in a fragment of bounded arithmetic that includes the injective weak pigeonhole principle for polynomial time functions, and also in a fragment that includes the surjective weak pigeonhole principle for FP NP functions. 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We further give new propositional translations, in terms of random resolution refutations, for the consequences of T 1 2 augmented with the surjective weak pigeon-hole principle for polynomial time functions.","internal_url":"https://www.academia.edu/21480109/FRAGMENTS_OF_APPROXIMATE_COUNTING","translated_internal_url":"","created_at":"2016-02-02T14:51:44.256-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":5937540,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"FRAGMENTS_OF_APPROXIMATE_COUNTING","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":"ABSTRACT We study the long-standing open problem of giving ∀Σ b 1 separa-tions for fragments of bounded arithmetic in the relativized setting. Rather than considering the usual fragments defined by the amount of induction they allow, we study Jeřábek\u0026amp;#39;s theories for approximate counting and their subtheories. We show that the ∀Σ b 1 Herbrandized ordering principle is unprovable in a fragment of bounded arithmetic that includes the injective weak pigeonhole principle for polynomial time functions, and also in a fragment that includes the surjective weak pigeonhole principle for FP NP functions. We further give new propositional translations, in terms of random resolution refutations, for the consequences of T 1 2 augmented with the surjective weak pigeon-hole principle for polynomial time functions.","owner":{"id":5937540,"first_name":"Sam","middle_initials":null,"last_name":"Buss","page_name":"SamBuss","domain_name":"ucsd","created_at":"2013-10-04T05:16:03.538-07:00","display_name":"Sam Buss","url":"https://ucsd.academia.edu/SamBuss"},"attachments":[],"research_interests":[{"id":803,"name":"Philosophy","url":"https://www.academia.edu/Documents/in/Philosophy"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"},{"id":179292,"name":"Symbolic Logic","url":"https://www.academia.edu/Documents/in/Symbolic_Logic"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="21480108"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/21480108/Short_Proofs_of_the_Kneser_Lov%C3%A1sz_Coloring_Principle"><img alt="Research paper thumbnail of Short Proofs of the Kneser-Lovász Coloring Principle" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480108/Short_Proofs_of_the_Kneser_Lov%C3%A1sz_Coloring_Principle">Short Proofs of the Kneser-Lovász Coloring Principle</a></div><div class="wp-workCard_item"><span>Lecture Notes in Computer Science</span><span>, 2015</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT We prove that the propositional translations of the Kneser-Lov\&amp;#39;asz theorem have...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT We prove that the propositional translations of the Kneser-Lov\&amp;#39;asz theorem have polynomial size extended Frege proofs and quasi-polynomial size Frege proofs. We present a new counting-based combinatorial proof of the Kneser-Lov\&amp;#39;asz theorem that avoids the topological arguments of prior proofs for all but finitely many cases for each k. We introduce a miniaturization of the octahedral Tucker lemma, called the truncated Tucker lemma: it is open whether its propositional translations have (quasi-)polynomial size Frege or extended Frege proofs.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480108"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480108"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480108; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=21480108]").text(description); $(".js-view-count[data-work-id=21480108]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 21480108; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='21480108']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 21480108, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=21480108]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":21480108,"title":"Short Proofs of the Kneser-Lovász Coloring Principle","translated_title":"","metadata":{"abstract":"ABSTRACT We prove that the propositional translations of the Kneser-Lov\\\u0026amp;#39;asz theorem have polynomial size extended Frege proofs and quasi-polynomial size Frege proofs. We present a new counting-based combinatorial proof of the Kneser-Lov\\\u0026amp;#39;asz theorem that avoids the topological arguments of prior proofs for all but finitely many cases for each k. We introduce a miniaturization of the octahedral Tucker lemma, called the truncated Tucker lemma: it is open whether its propositional translations have (quasi-)polynomial size Frege or extended Frege proofs.","publication_date":{"day":null,"month":null,"year":2015,"errors":{}},"publication_name":"Lecture Notes in Computer Science"},"translated_abstract":"ABSTRACT We prove that the propositional translations of the Kneser-Lov\\\u0026amp;#39;asz theorem have polynomial size extended Frege proofs and quasi-polynomial size Frege proofs. We present a new counting-based combinatorial proof of the Kneser-Lov\\\u0026amp;#39;asz theorem that avoids the topological arguments of prior proofs for all but finitely many cases for each k. We introduce a miniaturization of the octahedral Tucker lemma, called the truncated Tucker lemma: it is open whether its propositional translations have (quasi-)polynomial size Frege or extended Frege proofs.","internal_url":"https://www.academia.edu/21480108/Short_Proofs_of_the_Kneser_Lov%C3%A1sz_Coloring_Principle","translated_internal_url":"","created_at":"2016-02-02T14:51:44.048-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":5937540,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"Short_Proofs_of_the_Kneser_Lovász_Coloring_Principle","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":"ABSTRACT We prove that the propositional translations of the Kneser-Lov\\\u0026amp;#39;asz theorem have polynomial size extended Frege proofs and quasi-polynomial size Frege proofs. We present a new counting-based combinatorial proof of the Kneser-Lov\\\u0026amp;#39;asz theorem that avoids the topological arguments of prior proofs for all but finitely many cases for each k. We introduce a miniaturization of the octahedral Tucker lemma, called the truncated Tucker lemma: it is open whether its propositional translations have (quasi-)polynomial size Frege or extended Frege proofs.","owner":{"id":5937540,"first_name":"Sam","middle_initials":null,"last_name":"Buss","page_name":"SamBuss","domain_name":"ucsd","created_at":"2013-10-04T05:16:03.538-07:00","display_name":"Sam Buss","url":"https://ucsd.academia.edu/SamBuss"},"attachments":[],"research_interests":[],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="21480107"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/21480107/Sub_computable_Boundedness_Randomness"><img alt="Research paper thumbnail of Sub-computable Boundedness Randomness" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480107/Sub_computable_Boundedness_Randomness">Sub-computable Boundedness Randomness</a></div><div class="wp-workCard_item"><span>Logical Methods in Computer Science</span><span>, 2014</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT This paper defines a new notion of bounded computable randomness for certain classes of ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT This paper defines a new notion of bounded computable randomness for certain classes of sub-computable functions which lack a universal machine. In particular, we define such versions of randomness for primitive recursive functions and for PSPACE functions. These new notions are robust in that there are equivalent formulations in terms of (1) Martin-L\&amp;quot;of tests, (2) Kolmogorov complexity, and (3) martingales. We show these notions can be equivalently defined with prefix-free Kolmogorov complexity. We prove that one direction of van Lambalgen&amp;#39;s theorem holds for relative computability, but the other direction fails. We discuss statistical properties of these notions of randomness.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480107"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480107"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480107; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=21480107]").text(description); $(".js-view-count[data-work-id=21480107]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 21480107; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='21480107']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 21480107, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=21480107]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":21480107,"title":"Sub-computable Boundedness Randomness","translated_title":"","metadata":{"abstract":"ABSTRACT This paper defines a new notion of bounded computable randomness for certain classes of sub-computable functions which lack a universal machine. In particular, we define such versions of randomness for primitive recursive functions and for PSPACE functions. These new notions are robust in that there are equivalent formulations in terms of (1) Martin-L\\\u0026amp;quot;of tests, (2) Kolmogorov complexity, and (3) martingales. We show these notions can be equivalently defined with prefix-free Kolmogorov complexity. We prove that one direction of van Lambalgen\u0026amp;#39;s theorem holds for relative computability, but the other direction fails. We discuss statistical properties of these notions of randomness.","publication_date":{"day":null,"month":null,"year":2014,"errors":{}},"publication_name":"Logical Methods in Computer Science"},"translated_abstract":"ABSTRACT This paper defines a new notion of bounded computable randomness for certain classes of sub-computable functions which lack a universal machine. In particular, we define such versions of randomness for primitive recursive functions and for PSPACE functions. These new notions are robust in that there are equivalent formulations in terms of (1) Martin-L\\\u0026amp;quot;of tests, (2) Kolmogorov complexity, and (3) martingales. We show these notions can be equivalently defined with prefix-free Kolmogorov complexity. We prove that one direction of van Lambalgen\u0026amp;#39;s theorem holds for relative computability, but the other direction fails. We discuss statistical properties of these notions of randomness.","internal_url":"https://www.academia.edu/21480107/Sub_computable_Boundedness_Randomness","translated_internal_url":"","created_at":"2016-02-02T14:51:43.803-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":5937540,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"Sub_computable_Boundedness_Randomness","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":"ABSTRACT This paper defines a new notion of bounded computable randomness for certain classes of sub-computable functions which lack a universal machine. In particular, we define such versions of randomness for primitive recursive functions and for PSPACE functions. These new notions are robust in that there are equivalent formulations in terms of (1) Martin-L\\\u0026amp;quot;of tests, (2) Kolmogorov complexity, and (3) martingales. We show these notions can be equivalently defined with prefix-free Kolmogorov complexity. We prove that one direction of van Lambalgen\u0026amp;#39;s theorem holds for relative computability, but the other direction fails. We discuss statistical properties of these notions of randomness.","owner":{"id":5937540,"first_name":"Sam","middle_initials":null,"last_name":"Buss","page_name":"SamBuss","domain_name":"ucsd","created_at":"2013-10-04T05:16:03.538-07:00","display_name":"Sam Buss","url":"https://ucsd.academia.edu/SamBuss"},"attachments":[],"research_interests":[{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"},{"id":64561,"name":"Computer Software","url":"https://www.academia.edu/Documents/in/Computer_Software"},{"id":132545,"name":"Logical Methods in Computer Science","url":"https://www.academia.edu/Documents/in/Logical_Methods_in_Computer_Science"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="21480106"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/21480106/Collapsing_modular_counting_in_bounded_arithmetic_and_constant_depth_propositional_proofs"><img alt="Research paper thumbnail of Collapsing modular counting in bounded arithmetic and constant depth propositional proofs" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480106/Collapsing_modular_counting_in_bounded_arithmetic_and_constant_depth_propositional_proofs">Collapsing modular counting in bounded arithmetic and constant depth propositional proofs</a></div><div class="wp-workCard_item"><span>Transactions of the American Mathematical Society</span><span>, 2015</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480106"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480106"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480106; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=21480106]").text(description); $(".js-view-count[data-work-id=21480106]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 21480106; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='21480106']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 21480106, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=21480106]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":21480106,"title":"Collapsing modular counting in bounded arithmetic and constant depth propositional proofs","translated_title":"","metadata":{"publication_date":{"day":null,"month":null,"year":2015,"errors":{}},"publication_name":"Transactions of the American Mathematical Society"},"translated_abstract":null,"internal_url":"https://www.academia.edu/21480106/Collapsing_modular_counting_in_bounded_arithmetic_and_constant_depth_propositional_proofs","translated_internal_url":"","created_at":"2016-02-02T14:51:43.343-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":5937540,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"Collapsing_modular_counting_in_bounded_arithmetic_and_constant_depth_propositional_proofs","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":null,"owner":{"id":5937540,"first_name":"Sam","middle_initials":null,"last_name":"Buss","page_name":"SamBuss","domain_name":"ucsd","created_at":"2013-10-04T05:16:03.538-07:00","display_name":"Sam Buss","url":"https://ucsd.academia.edu/SamBuss"},"attachments":[],"research_interests":[{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="21480105"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/21480105/Book_Review_Matthias_Baaz_and_Alexander_Leitsch_Methods_of_Cut_Elimination"><img alt="Research paper thumbnail of Book Review: Matthias Baaz and Alexander Leitsch, Methods of Cut-Elimination" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480105/Book_Review_Matthias_Baaz_and_Alexander_Leitsch_Methods_of_Cut_Elimination">Book Review: Matthias Baaz and Alexander Leitsch, Methods of Cut-Elimination</a></div><div class="wp-workCard_item"><span>Studia Logica</span><span>, 2015</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480105"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480105"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480105; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="21480104"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/21480104/Limits_on_Alternation_Trading_Proofs_for_Time_Space_Lower_Bounds"><img alt="Research paper thumbnail of Limits on Alternation-Trading Proofs for Time-Space Lower Bounds" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480104/Limits_on_Alternation_Trading_Proofs_for_Time_Space_Lower_Bounds">Limits on Alternation-Trading Proofs for Time-Space Lower Bounds</a></div><div class="wp-workCard_item"><span>2012 IEEE 27th Conference on Computational Complexity</span><span>, 2012</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480104"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480104"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480104; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="21480103"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/21480103/Resolution_and_the_weak_pigeonhole_principle"><img alt="Research paper thumbnail of Resolution and the weak pigeonhole principle" class="work-thumbnail" src="https://attachments.academia-assets.com/41904054/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480103/Resolution_and_the_weak_pigeonhole_principle">Resolution and the weak pigeonhole principle</a></div><div class="wp-workCard_item"><span>Lecture Notes in Computer Science</span><span>, 1998</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We give new upper bounds for resolution proofs of the weak pigeonhole principle. We also give low...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We give new upper bounds for resolution proofs of the weak pigeonhole principle. We also give lower bounds for tree-like resolution proofs. We present a normal form for resolution proofs of pigeonhole principles based on a new monotone resolution rule. n ; in other words,</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="2fa1e798472a78ba49884cd06bc983b5" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41904054,"asset_id":21480103,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41904054/download_file?st=MTczNDU0MTQ1OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480103"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480103"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480103; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=21480103]").text(description); $(".js-view-count[data-work-id=21480103]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 21480103; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='21480103']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 21480103, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "2fa1e798472a78ba49884cd06bc983b5" } } $('.js-work-strip[data-work-id=21480103]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":21480103,"title":"Resolution and the weak pigeonhole principle","translated_title":"","metadata":{"grobid_abstract":"We give new upper bounds for resolution proofs of the weak pigeonhole principle. 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We present a normal form for resolution proofs of pigeonhole principles based on a new monotone resolution rule. n ; in other words,","owner":{"id":5937540,"first_name":"Sam","middle_initials":null,"last_name":"Buss","page_name":"SamBuss","domain_name":"ucsd","created_at":"2013-10-04T05:16:03.538-07:00","display_name":"Sam Buss","url":"https://ucsd.academia.edu/SamBuss"},"attachments":[{"id":41904054,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41904054/thumbnails/1.jpg","file_name":"paper.pdf","download_url":"https://www.academia.edu/attachments/41904054/download_file?st=MTczNDU0MTQ1OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Resolution_and_the_weak_pigeonhole_princ.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41904054/paper-libre.pdf?1454453897=\u0026response-content-disposition=attachment%3B+filename%3DResolution_and_the_weak_pigeonhole_princ.pdf\u0026Expires=1734545058\u0026Signature=A-2RcaZe6RrnyaEqJOnWppGbVKw09CRdZq94qZtmDMvJVdtLbkV9P9ytC3n82h2SvmdEW2ehOyC-UNG~Lv3kA8y-rfuuuOMEnQmSZw-Q99F9XfldrvBOWlBAYzFv8bxqXDqgCGQfl1F7e7e1L6dev7ly57RrK44x8Hg7hau-PB3bpu1T1KcsFrstGvvZbe6MrclgacRqAn0~KMR8DyZLJ9gR8MfiWzSYjtZlSw1Ls9QtlMaKb60DBkgGKoeAwnBLN88PWyeCwD0StJIy-gjtif6CIF~AAo8EPlbAHT2vAkRVF7TuHPn2t~m7eYbDfGBCpB0420iuAO8F1VqoUjm54g__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":571143,"name":"Lower Bound","url":"https://www.academia.edu/Documents/in/Lower_Bound"},{"id":575846,"name":"Upper Bound","url":"https://www.academia.edu/Documents/in/Upper_Bound"},{"id":2132350,"name":"Normal Form","url":"https://www.academia.edu/Documents/in/Normal_Form"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="21480102"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/21480102/THE_POLYNOMIAL_HIERARCHY_AND_INTUITIONISTIC_BOUNDED_ARITHMETIC"><img alt="Research paper thumbnail of THE POLYNOMIAL HIERARCHY AND INTUITIONISTIC BOUNDED ARITHMETIC" class="work-thumbnail" src="https://attachments.academia-assets.com/41904057/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480102/THE_POLYNOMIAL_HIERARCHY_AND_INTUITIONISTIC_BOUNDED_ARITHMETIC">THE POLYNOMIAL HIERARCHY AND INTUITIONISTIC BOUNDED ARITHMETIC</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Intuitionistic theories IS: of Bounded Arithmetic a r e introduced and i t is shown t h a t the d...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Intuitionistic theories IS: of Bounded Arithmetic a r e introduced and i t is shown t h a t the definable functions of IS: a r e precisely the 0: functions of t h e polvnomial hierarchy. This is an extension of earlier work on t h e classical Bounded Arithmetic and was first conjectured by S. Cook. In contrast t o t h e classical theories of Bounded b Arithmetic where Ci-definable functions are of interest, our results for intuitionistic theories concern all the definable functions. The method of proof uses 0;-realizability which is inspired by t h e recursive realizability of S.C. Kleene 131 and D. Nelson 151. I t also involves polynomial hierarchy functionals of finite type which a r e introduced in this paper. * Research supported in part by NSF Grant DMS 85-11465. In general, 0: is P The theories Si a r e most advantageously viewed a s Gentzen-style natural deduction systems. A formal proof in a natural deduction system contains sequents of t h e form where each A. and B. is a formula. The meaning of such a sequent is J J In addition t o t h e usual inference rules for natural deduction. the Z:-PIND inference is b</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="c80a4a8736875be8e1f9f6d18234e1a1" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41904057,"asset_id":21480102,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41904057/download_file?st=MTczNDU0MTQ1OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480102"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480102"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480102; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=21480102]").text(description); $(".js-view-count[data-work-id=21480102]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 21480102; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='21480102']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 21480102, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "c80a4a8736875be8e1f9f6d18234e1a1" } } $('.js-work-strip[data-work-id=21480102]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":21480102,"title":"THE POLYNOMIAL HIERARCHY AND INTUITIONISTIC BOUNDED ARITHMETIC","translated_title":"","metadata":{"grobid_abstract":"Intuitionistic theories IS: of Bounded Arithmetic a r e introduced and i t is shown t h a t the definable functions of IS: a r e precisely the 0: functions of t h e polvnomial hierarchy. 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Upper and lower bounds for first order expressibility. Journal of computer and system sciences, vol. 25 (1982), pp. 76–98. Immerman Neil. Relational queries computable in polynomial time. Information and control, vol. 68 (1986), pp. 86–104. Immerman Neil. Languages that capture com..." class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480101/Immerman_Neil_Upper_and_lower_bounds_for_first_order_expressibility_Journal_of_computer_and_system_sciences_vol_25_1982_pp_76_98_Immerman_Neil_Relational_queries_computable_in_polynomial_time_Information_and_control_vol_68_1986_pp_86_104_Immerman_Neil_Languages_that_capture_com_">Immerman Neil. Upper and lower bounds for first order expressibility. Journal of computer and system sciences, vol. 25 (1982), pp. 76–98. Immerman Neil. Relational queries computable in polynomial time. Information and control, vol. 68 (1986), pp. 86–104. Immerman Neil. Languages that capture com...</a></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480101"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480101"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480101; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=21480101]").text(description); $(".js-view-count[data-work-id=21480101]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 21480101; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='21480101']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 21480101, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=21480101]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":21480101,"title":"Immerman Neil. Upper and lower bounds for first order expressibility. Journal of computer and system sciences, vol. 25 (1982), pp. 76–98. Immerman Neil. Relational queries computable in polynomial time. Information and control, vol. 68 (1986), pp. 86–104. Immerman Neil. Languages that capture com...","translated_title":"","metadata":{},"translated_abstract":null,"internal_url":"https://www.academia.edu/21480101/Immerman_Neil_Upper_and_lower_bounds_for_first_order_expressibility_Journal_of_computer_and_system_sciences_vol_25_1982_pp_76_98_Immerman_Neil_Relational_queries_computable_in_polynomial_time_Information_and_control_vol_68_1986_pp_86_104_Immerman_Neil_Languages_that_capture_com_","translated_internal_url":"","created_at":"2016-02-02T14:51:42.038-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":5937540,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"Immerman_Neil_Upper_and_lower_bounds_for_first_order_expressibility_Journal_of_computer_and_system_sciences_vol_25_1982_pp_76_98_Immerman_Neil_Relational_queries_computable_in_polynomial_time_Information_and_control_vol_68_1986_pp_86_104_Immerman_Neil_Languages_that_capture_com_","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":null,"owner":{"id":5937540,"first_name":"Sam","middle_initials":null,"last_name":"Buss","page_name":"SamBuss","domain_name":"ucsd","created_at":"2013-10-04T05:16:03.538-07:00","display_name":"Sam Buss","url":"https://ucsd.academia.edu/SamBuss"},"attachments":[],"research_interests":[],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> </div><div class="profile--tab_content_container js-tab-pane tab-pane" data-section-id="789275" id="papers"><div class="js-work-strip profile--work_container" data-work-id="21480120"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/21480120/Cobham_recursive_set_functions"><img alt="Research paper thumbnail of Cobham recursive set functions" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480120/Cobham_recursive_set_functions">Cobham recursive set functions</a></div><div class="wp-workCard_item"><span>Annals of Pure and Applied Logic</span><span>, 2016</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480120"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480120"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480120; 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For propositional logic, this requires con-verting a proof from tree-like to dag-like form, but it most doubles the number of lines in the proof. For first-order logic, the proof size can grow exponentially, but the proof has a succinct description and is polynomial-time uniform. We use direct, global constructions that give polynomial time methods for removing all top-level cuts from proofs. By exploiting prenex representations, this extends to removing all cuts, with final proof size bounded superexponentially in the alternation of quantifiers in cut formulas.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480119"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480119"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480119; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=21480119]").text(description); $(".js-view-count[data-work-id=21480119]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 21480119; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='21480119']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 21480119, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=21480119]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":21480119,"title":"Cut Elimination In Situ","translated_title":"","metadata":{"abstract":"ABSTRACT We present methods for removing top-level cuts from a sequent calculus or Tait-style proof without significantly increasing the space used for storing the proof. 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By exploiting prenex representations, this extends to removing all cuts, with final proof size bounded superexponentially in the alternation of quantifiers in cut formulas.","internal_url":"https://www.academia.edu/21480119/Cut_Elimination_In_Situ","translated_internal_url":"","created_at":"2016-02-02T14:51:46.601-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":5937540,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"Cut_Elimination_In_Situ","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":"ABSTRACT We present methods for removing top-level cuts from a sequent calculus or Tait-style proof without significantly increasing the space used for storing the proof. For propositional logic, this requires con-verting a proof from tree-like to dag-like form, but it most doubles the number of lines in the proof. For first-order logic, the proof size can grow exponentially, but the proof has a succinct description and is polynomial-time uniform. We use direct, global constructions that give polynomial time methods for removing all top-level cuts from proofs. By exploiting prenex representations, this extends to removing all cuts, with final proof size bounded superexponentially in the alternation of quantifiers in cut formulas.","owner":{"id":5937540,"first_name":"Sam","middle_initials":null,"last_name":"Buss","page_name":"SamBuss","domain_name":"ucsd","created_at":"2013-10-04T05:16:03.538-07:00","display_name":"Sam Buss","url":"https://ucsd.academia.edu/SamBuss"},"attachments":[],"research_interests":[],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="21480118"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/21480118/Some_remarks_on_lengths_of_propositional_proofs"><img alt="Research paper thumbnail of Some remarks on lengths of propositional proofs" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480118/Some_remarks_on_lengths_of_propositional_proofs">Some remarks on lengths of propositional proofs</a></div><div class="wp-workCard_item"><span>Archive for Mathematical Logic</span><span>, 1995</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480118"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480118"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480118; 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dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=21480118]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":21480118,"title":"Some remarks on lengths of propositional proofs","translated_title":"","metadata":{"abstract":"ABSTRACT","publication_date":{"day":null,"month":null,"year":1995,"errors":{}},"publication_name":"Archive for Mathematical Logic"},"translated_abstract":"ABSTRACT","internal_url":"https://www.academia.edu/21480118/Some_remarks_on_lengths_of_propositional_proofs","translated_internal_url":"","created_at":"2016-02-02T14:51:46.411-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":5937540,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"Some_remarks_on_lengths_of_propositional_proofs","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":"ABSTRACT","owner":{"id":5937540,"first_name":"Sam","middle_initials":null,"last_name":"Buss","page_name":"SamBuss","domain_name":"ucsd","created_at":"2013-10-04T05:16:03.538-07:00","display_name":"Sam Buss","url":"https://ucsd.academia.edu/SamBuss"},"attachments":[],"research_interests":[{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"},{"id":349057,"name":"Sequent Calculus","url":"https://www.academia.edu/Documents/in/Sequent_Calculus"},{"id":571143,"name":"Lower Bound","url":"https://www.academia.edu/Documents/in/Lower_Bound"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="21480117"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/21480117/Alogtime_algorithms_for_tree_isomorphism_comparison_and_canonization"><img alt="Research paper thumbnail of Alogtime algorithms for tree isomorphism, comparison, and canonization" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480117/Alogtime_algorithms_for_tree_isomorphism_comparison_and_canonization">Alogtime algorithms for tree isomorphism, comparison, and canonization</a></div><div class="wp-workCard_item"><span>Lecture Notes in Computer Science</span><span>, 1997</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480117"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480117"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480117; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=21480117]").text(description); $(".js-view-count[data-work-id=21480117]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 21480117; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='21480117']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 21480117, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=21480117]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":21480117,"title":"Alogtime algorithms for tree isomorphism, comparison, and canonization","translated_title":"","metadata":{"abstract":"ABSTRACT","publication_date":{"day":null,"month":null,"year":1997,"errors":{}},"publication_name":"Lecture Notes in Computer Science"},"translated_abstract":"ABSTRACT","internal_url":"https://www.academia.edu/21480117/Alogtime_algorithms_for_tree_isomorphism_comparison_and_canonization","translated_internal_url":"","created_at":"2016-02-02T14:51:46.169-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":5937540,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"Alogtime_algorithms_for_tree_isomorphism_comparison_and_canonization","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":"ABSTRACT","owner":{"id":5937540,"first_name":"Sam","middle_initials":null,"last_name":"Buss","page_name":"SamBuss","domain_name":"ucsd","created_at":"2013-10-04T05:16:03.538-07:00","display_name":"Sam Buss","url":"https://ucsd.academia.edu/SamBuss"},"attachments":[],"research_interests":[],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="21480116"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/21480116/The_polynomial_hierarchy_and_intuitionistic_Bounded_Arithmetic"><img alt="Research paper thumbnail of The polynomial hierarchy and intuitionistic Bounded Arithmetic" class="work-thumbnail" src="https://attachments.academia-assets.com/41904058/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480116/The_polynomial_hierarchy_and_intuitionistic_Bounded_Arithmetic">The polynomial hierarchy and intuitionistic Bounded Arithmetic</a></div><div class="wp-workCard_item"><span>Lecture Notes in Computer Science</span><span>, 1986</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Intuitionistic theories IS: of Bounded Arithmetic a r e introduced and i t is shown t h a t the d...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Intuitionistic theories IS: of Bounded Arithmetic a r e introduced and i t is shown t h a t the definable functions of IS: a r e precisely the 0: functions of t h e polvnomial hierarchy. This is an extension of earlier work on t h e classical Bounded Arithmetic and was first conjectured by S. Cook. In contrast t o t h e classical theories of Bounded b Arithmetic where Ci-definable functions are of interest, our results for intuitionistic theories concern all the definable functions. The method of proof uses 0;-realizability which is inspired by t h e recursive realizability of S.C. Kleene 131 and D. Nelson 151. I t also involves polynomial hierarchy functionals of finite type which a r e introduced in this paper. * Research supported in part by NSF Grant DMS 85-11465. In general, 0: is P The theories Si a r e most advantageously viewed a s Gentzen-style natural deduction systems. A formal proof in a natural deduction system contains sequents of t h e form where each A. and B. is a formula. The meaning of such a sequent is J J In addition t o t h e usual inference rules for natural deduction. the Z:-PIND inference is b</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="bff228b6fcf217bc140bb172bfcba6e8" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41904058,"asset_id":21480116,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41904058/download_file?st=MTczNDU0MTQ1OCw4LjIyMi4yMDguMTQ2&st=MTczNDU0MTQ1OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480116"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480116"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480116; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=21480116]").text(description); $(".js-view-count[data-work-id=21480116]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 21480116; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='21480116']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 21480116, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "bff228b6fcf217bc140bb172bfcba6e8" } } $('.js-work-strip[data-work-id=21480116]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":21480116,"title":"The polynomial hierarchy and intuitionistic Bounded Arithmetic","translated_title":"","metadata":{"grobid_abstract":"Intuitionistic theories IS: of Bounded Arithmetic a r e introduced and i t is shown t h a t the definable functions of IS: a r e precisely the 0: functions of t h e polvnomial hierarchy. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="21480113"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/21480113/The_Computational_Power_of_Bounded_Arithmetic_from_the_Predicative_Viewpoint"><img alt="Research paper thumbnail of The Computational Power of Bounded Arithmetic from the Predicative Viewpoint" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480113/The_Computational_Power_of_Bounded_Arithmetic_from_the_Predicative_Viewpoint">The Computational Power of Bounded Arithmetic from the Predicative Viewpoint</a></div><div class="wp-workCard_item"><span>New Computational Paradigms</span><span>, 2008</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT This paper considers theories of bounded arithmetic that are predicative in the sense of...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT This paper considers theories of bounded arithmetic that are predicative in the sense of Nelson, that is, theories that are interpretable in Robinson’s Q.We give a nearly exact characterization of functions that can be total in predicative bounded theories. As an upper bound, any such function has a polynomial growth rate and its bit-graph is in nondeterministic exponential time and in co-nondeterministic exponential time. In fact, any function uniquely defined in a bounded theory of arithmetic lies in this class. Conversely, any function that is in this class (provably in IΔ0+exp) can be uniquely defined and total in a (predicative) bounded theory of arithmetic.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480113"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480113"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480113; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=21480113]").text(description); $(".js-view-count[data-work-id=21480113]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 21480113; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='21480113']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 21480113, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=21480113]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":21480113,"title":"The Computational Power of Bounded Arithmetic from the Predicative Viewpoint","translated_title":"","metadata":{"abstract":"ABSTRACT This paper considers theories of bounded arithmetic that are predicative in the sense of Nelson, that is, theories that are interpretable in Robinson’s Q.We give a nearly exact characterization of functions that can be total in predicative bounded theories. 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In fact, any function uniquely defined in a bounded theory of arithmetic lies in this class. Conversely, any function that is in this class (provably in IΔ0+exp) can be uniquely defined and total in a (predicative) bounded theory of arithmetic.","internal_url":"https://www.academia.edu/21480113/The_Computational_Power_of_Bounded_Arithmetic_from_the_Predicative_Viewpoint","translated_internal_url":"","created_at":"2016-02-02T14:51:45.108-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":5937540,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"The_Computational_Power_of_Bounded_Arithmetic_from_the_Predicative_Viewpoint","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":"ABSTRACT This paper considers theories of bounded arithmetic that are predicative in the sense of Nelson, that is, theories that are interpretable in Robinson’s Q.We give a nearly exact characterization of functions that can be total in predicative bounded theories. 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Conversely, any function that is in this class (provably in IΔ0+exp) can be uniquely defined and total in a (predicative) bounded theory of arithmetic.","owner":{"id":5937540,"first_name":"Sam","middle_initials":null,"last_name":"Buss","page_name":"SamBuss","domain_name":"ucsd","created_at":"2013-10-04T05:16:03.538-07:00","display_name":"Sam Buss","url":"https://ucsd.academia.edu/SamBuss"},"attachments":[],"research_interests":[],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="21480112"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/21480112/On_Model_Theory_for_Intuitionistic_Bounded_Arithmetic_with_Applications_to_Independence_Results"><img alt="Research paper thumbnail of On Model Theory for Intuitionistic Bounded Arithmetic with Applications to Independence Results" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480112/On_Model_Theory_for_Intuitionistic_Bounded_Arithmetic_with_Applications_to_Independence_Results">On Model Theory for Intuitionistic Bounded Arithmetic with Applications to Independence Results</a></div><div class="wp-workCard_item"><span>Feasible Mathematics</span><span>, 1990</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">... It is open whether the theory CPV= S\(PV) can prove NPB ... Mi^ M} if and only if i i&lt; j. ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">... It is open whether the theory CPV= S\(PV) can prove NPB ... Mi^ M} if and only if i i&lt; j. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="21480110"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/21480110/A_note_on_bootstrapping_intuitionistic_bounded_arithmetic"><img alt="Research paper thumbnail of A note on bootstrapping intuitionistic bounded arithmetic" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480110/A_note_on_bootstrapping_intuitionistic_bounded_arithmetic">A note on bootstrapping intuitionistic bounded arithmetic</a></div><div class="wp-workCard_item"><span>A selection of papers from the Leeds Proof Theory Programme 1990</span><span>, 1993</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480110"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480110"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480110; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="21480109"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/21480109/FRAGMENTS_OF_APPROXIMATE_COUNTING"><img alt="Research paper thumbnail of FRAGMENTS OF APPROXIMATE COUNTING" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480109/FRAGMENTS_OF_APPROXIMATE_COUNTING">FRAGMENTS OF APPROXIMATE COUNTING</a></div><div class="wp-workCard_item"><span>The Journal of Symbolic Logic</span><span>, 2014</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT We study the long-standing open problem of giving ∀Σ b 1 separa-tions for fragments of b...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT We study the long-standing open problem of giving ∀Σ b 1 separa-tions for fragments of bounded arithmetic in the relativized setting. Rather than considering the usual fragments defined by the amount of induction they allow, we study Jeřábek&amp;#39;s theories for approximate counting and their subtheories. We show that the ∀Σ b 1 Herbrandized ordering principle is unprovable in a fragment of bounded arithmetic that includes the injective weak pigeonhole principle for polynomial time functions, and also in a fragment that includes the surjective weak pigeonhole principle for FP NP functions. We further give new propositional translations, in terms of random resolution refutations, for the consequences of T 1 2 augmented with the surjective weak pigeon-hole principle for polynomial time functions.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480109"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480109"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480109; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=21480109]").text(description); $(".js-view-count[data-work-id=21480109]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 21480109; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='21480109']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 21480109, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=21480109]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":21480109,"title":"FRAGMENTS OF APPROXIMATE COUNTING","translated_title":"","metadata":{"abstract":"ABSTRACT We study the long-standing open problem of giving ∀Σ b 1 separa-tions for fragments of bounded arithmetic in the relativized setting. 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We further give new propositional translations, in terms of random resolution refutations, for the consequences of T 1 2 augmented with the surjective weak pigeon-hole principle for polynomial time functions.","internal_url":"https://www.academia.edu/21480109/FRAGMENTS_OF_APPROXIMATE_COUNTING","translated_internal_url":"","created_at":"2016-02-02T14:51:44.256-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":5937540,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"FRAGMENTS_OF_APPROXIMATE_COUNTING","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":"ABSTRACT We study the long-standing open problem of giving ∀Σ b 1 separa-tions for fragments of bounded arithmetic in the relativized setting. 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We further give new propositional translations, in terms of random resolution refutations, for the consequences of T 1 2 augmented with the surjective weak pigeon-hole principle for polynomial time functions.","owner":{"id":5937540,"first_name":"Sam","middle_initials":null,"last_name":"Buss","page_name":"SamBuss","domain_name":"ucsd","created_at":"2013-10-04T05:16:03.538-07:00","display_name":"Sam Buss","url":"https://ucsd.academia.edu/SamBuss"},"attachments":[],"research_interests":[{"id":803,"name":"Philosophy","url":"https://www.academia.edu/Documents/in/Philosophy"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"},{"id":179292,"name":"Symbolic Logic","url":"https://www.academia.edu/Documents/in/Symbolic_Logic"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="21480108"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/21480108/Short_Proofs_of_the_Kneser_Lov%C3%A1sz_Coloring_Principle"><img alt="Research paper thumbnail of Short Proofs of the Kneser-Lovász Coloring Principle" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480108/Short_Proofs_of_the_Kneser_Lov%C3%A1sz_Coloring_Principle">Short Proofs of the Kneser-Lovász Coloring Principle</a></div><div class="wp-workCard_item"><span>Lecture Notes in Computer Science</span><span>, 2015</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT We prove that the propositional translations of the Kneser-Lov\&amp;#39;asz theorem have...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT We prove that the propositional translations of the Kneser-Lov\&amp;#39;asz theorem have polynomial size extended Frege proofs and quasi-polynomial size Frege proofs. We present a new counting-based combinatorial proof of the Kneser-Lov\&amp;#39;asz theorem that avoids the topological arguments of prior proofs for all but finitely many cases for each k. We introduce a miniaturization of the octahedral Tucker lemma, called the truncated Tucker lemma: it is open whether its propositional translations have (quasi-)polynomial size Frege or extended Frege proofs.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480108"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480108"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480108; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=21480108]").text(description); $(".js-view-count[data-work-id=21480108]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 21480108; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='21480108']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 21480108, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=21480108]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":21480108,"title":"Short Proofs of the Kneser-Lovász Coloring Principle","translated_title":"","metadata":{"abstract":"ABSTRACT We prove that the propositional translations of the Kneser-Lov\\\u0026amp;#39;asz theorem have polynomial size extended Frege proofs and quasi-polynomial size Frege proofs. We present a new counting-based combinatorial proof of the Kneser-Lov\\\u0026amp;#39;asz theorem that avoids the topological arguments of prior proofs for all but finitely many cases for each k. We introduce a miniaturization of the octahedral Tucker lemma, called the truncated Tucker lemma: it is open whether its propositional translations have (quasi-)polynomial size Frege or extended Frege proofs.","publication_date":{"day":null,"month":null,"year":2015,"errors":{}},"publication_name":"Lecture Notes in Computer Science"},"translated_abstract":"ABSTRACT We prove that the propositional translations of the Kneser-Lov\\\u0026amp;#39;asz theorem have polynomial size extended Frege proofs and quasi-polynomial size Frege proofs. We present a new counting-based combinatorial proof of the Kneser-Lov\\\u0026amp;#39;asz theorem that avoids the topological arguments of prior proofs for all but finitely many cases for each k. We introduce a miniaturization of the octahedral Tucker lemma, called the truncated Tucker lemma: it is open whether its propositional translations have (quasi-)polynomial size Frege or extended Frege proofs.","internal_url":"https://www.academia.edu/21480108/Short_Proofs_of_the_Kneser_Lov%C3%A1sz_Coloring_Principle","translated_internal_url":"","created_at":"2016-02-02T14:51:44.048-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":5937540,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"Short_Proofs_of_the_Kneser_Lovász_Coloring_Principle","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":"ABSTRACT We prove that the propositional translations of the Kneser-Lov\\\u0026amp;#39;asz theorem have polynomial size extended Frege proofs and quasi-polynomial size Frege proofs. We present a new counting-based combinatorial proof of the Kneser-Lov\\\u0026amp;#39;asz theorem that avoids the topological arguments of prior proofs for all but finitely many cases for each k. We introduce a miniaturization of the octahedral Tucker lemma, called the truncated Tucker lemma: it is open whether its propositional translations have (quasi-)polynomial size Frege or extended Frege proofs.","owner":{"id":5937540,"first_name":"Sam","middle_initials":null,"last_name":"Buss","page_name":"SamBuss","domain_name":"ucsd","created_at":"2013-10-04T05:16:03.538-07:00","display_name":"Sam Buss","url":"https://ucsd.academia.edu/SamBuss"},"attachments":[],"research_interests":[],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="21480107"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/21480107/Sub_computable_Boundedness_Randomness"><img alt="Research paper thumbnail of Sub-computable Boundedness Randomness" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480107/Sub_computable_Boundedness_Randomness">Sub-computable Boundedness Randomness</a></div><div class="wp-workCard_item"><span>Logical Methods in Computer Science</span><span>, 2014</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT This paper defines a new notion of bounded computable randomness for certain classes of ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT This paper defines a new notion of bounded computable randomness for certain classes of sub-computable functions which lack a universal machine. In particular, we define such versions of randomness for primitive recursive functions and for PSPACE functions. These new notions are robust in that there are equivalent formulations in terms of (1) Martin-L\&amp;quot;of tests, (2) Kolmogorov complexity, and (3) martingales. We show these notions can be equivalently defined with prefix-free Kolmogorov complexity. We prove that one direction of van Lambalgen&amp;#39;s theorem holds for relative computability, but the other direction fails. We discuss statistical properties of these notions of randomness.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480107"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480107"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480107; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=21480107]").text(description); $(".js-view-count[data-work-id=21480107]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 21480107; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='21480107']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 21480107, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=21480107]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":21480107,"title":"Sub-computable Boundedness Randomness","translated_title":"","metadata":{"abstract":"ABSTRACT This paper defines a new notion of bounded computable randomness for certain classes of sub-computable functions which lack a universal machine. 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These new notions are robust in that there are equivalent formulations in terms of (1) Martin-L\\\u0026amp;quot;of tests, (2) Kolmogorov complexity, and (3) martingales. We show these notions can be equivalently defined with prefix-free Kolmogorov complexity. We prove that one direction of van Lambalgen\u0026amp;#39;s theorem holds for relative computability, but the other direction fails. We discuss statistical properties of these notions of randomness.","internal_url":"https://www.academia.edu/21480107/Sub_computable_Boundedness_Randomness","translated_internal_url":"","created_at":"2016-02-02T14:51:43.803-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":5937540,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"Sub_computable_Boundedness_Randomness","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":"ABSTRACT This paper defines a new notion of bounded computable randomness for certain classes of sub-computable functions which lack a universal machine. In particular, we define such versions of randomness for primitive recursive functions and for PSPACE functions. These new notions are robust in that there are equivalent formulations in terms of (1) Martin-L\\\u0026amp;quot;of tests, (2) Kolmogorov complexity, and (3) martingales. We show these notions can be equivalently defined with prefix-free Kolmogorov complexity. We prove that one direction of van Lambalgen\u0026amp;#39;s theorem holds for relative computability, but the other direction fails. 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We also give low...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We give new upper bounds for resolution proofs of the weak pigeonhole principle. We also give lower bounds for tree-like resolution proofs. We present a normal form for resolution proofs of pigeonhole principles based on a new monotone resolution rule. n ; in other words,</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="2fa1e798472a78ba49884cd06bc983b5" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41904054,"asset_id":21480103,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41904054/download_file?st=MTczNDU0MTQ1OCw4LjIyMi4yMDguMTQ2&st=MTczNDU0MTQ1OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480103"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480103"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480103; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=21480103]").text(description); $(".js-view-count[data-work-id=21480103]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 21480103; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='21480103']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 21480103, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "2fa1e798472a78ba49884cd06bc983b5" } } $('.js-work-strip[data-work-id=21480103]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":21480103,"title":"Resolution and the weak pigeonhole principle","translated_title":"","metadata":{"grobid_abstract":"We give new upper bounds for resolution proofs of the weak pigeonhole principle. 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This is an extension of earlier work on t h e classical Bounded Arithmetic and was first conjectured by S. Cook. In contrast t o t h e classical theories of Bounded b Arithmetic where Ci-definable functions are of interest, our results for intuitionistic theories concern all the definable functions. The method of proof uses 0;-realizability which is inspired by t h e recursive realizability of S.C. Kleene 131 and D. Nelson 151. I t also involves polynomial hierarchy functionals of finite type which a r e introduced in this paper. * Research supported in part by NSF Grant DMS 85-11465. In general, 0: is P The theories Si a r e most advantageously viewed a s Gentzen-style natural deduction systems. A formal proof in a natural deduction system contains sequents of t h e form where each A. and B. is a formula. The meaning of such a sequent is J J In addition t o t h e usual inference rules for natural deduction. the Z:-PIND inference is b</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="c80a4a8736875be8e1f9f6d18234e1a1" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41904057,"asset_id":21480102,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41904057/download_file?st=MTczNDU0MTQ1OCw4LjIyMi4yMDguMTQ2&st=MTczNDU0MTQ1OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="21480102"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="21480102"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21480102; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=21480102]").text(description); $(".js-view-count[data-work-id=21480102]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 21480102; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='21480102']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 21480102, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "c80a4a8736875be8e1f9f6d18234e1a1" } } $('.js-work-strip[data-work-id=21480102]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":21480102,"title":"THE POLYNOMIAL HIERARCHY AND INTUITIONISTIC BOUNDED ARITHMETIC","translated_title":"","metadata":{"grobid_abstract":"Intuitionistic theories IS: of Bounded Arithmetic a r e introduced and i t is shown t h a t the definable functions of IS: a r e precisely the 0: functions of t h e polvnomial hierarchy. 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Upper and lower bounds for first order expressibility. Journal of computer and system sciences, vol. 25 (1982), pp. 76–98. Immerman Neil. Relational queries computable in polynomial time. Information and control, vol. 68 (1986), pp. 86–104. Immerman Neil. Languages that capture com..." class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/21480101/Immerman_Neil_Upper_and_lower_bounds_for_first_order_expressibility_Journal_of_computer_and_system_sciences_vol_25_1982_pp_76_98_Immerman_Neil_Relational_queries_computable_in_polynomial_time_Information_and_control_vol_68_1986_pp_86_104_Immerman_Neil_Languages_that_capture_com_">Immerman Neil. Upper and lower bounds for first order expressibility. Journal of computer and system sciences, vol. 25 (1982), pp. 76–98. Immerman Neil. Relational queries computable in polynomial time. Information and control, vol. 68 (1986), pp. 86–104. Immerman Neil. 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Upper and lower bounds for first order expressibility. Journal of computer and system sciences, vol. 25 (1982), pp. 76–98. Immerman Neil. Relational queries computable in polynomial time. Information and control, vol. 68 (1986), pp. 86–104. Immerman Neil. 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