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(PDF) A Tight Lower Bound for Determinization of Transition Labeled Büchi Automata | Konrad Zdanowski - Academia.edu
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We highlight directions that have broad implications across game theory, automata theory, and AI.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Game-Theoretic Automata: Foundations, Formalizations, and Open Problems","attachmentId":120079784,"attachmentType":"pdf","work_url":"https://www.academia.edu/126160020/Game_Theoretic_Automata_Foundations_Formalizations_and_Open_Problems","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/126160020/Game_Theoretic_Automata_Foundations_Formalizations_and_Open_Problems"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="25478810" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/25478810/Banach_Mazur_Games_on_Graphs">Banach-Mazur Games on Graphs</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="48906363" href="https://rwth-aachen.academia.edu/ErichGr%C3%A4del">Erich Grädel</a></div><p class="ds-related-work--abstract ds2-5-body-sm">We survey determinacy, definability, and complexity issues of Banach-Mazur games on finite and infinite graphs. Infinite games where two players take turns to move a token through a directed graph, thus tracing out an infinite path, have numerous applications in different branches of mathematics and computer science. In the usual format, the possible moves of the players are given by the edges of the graph; in each move a player takes the token from its current position along an edge to a next position. In Banach-Mazur games the players instead select in each move a emph{path} of arbitrary finite length rather than just an edge. In both cases the outcome of a play is an infinite path. A winning condition is thus given by a set of infinite paths which is often specified by a logical formula, for instance from S1S, LTL, or first-order logic. Banach-Mazur games have a long tradition in descriptive set theory and topology, and they have recently been shown to have interesting applicatio...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Banach-Mazur Games on Graphs","attachmentId":45796914,"attachmentType":"pdf","work_url":"https://www.academia.edu/25478810/Banach_Mazur_Games_on_Graphs","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/25478810/Banach_Mazur_Games_on_Graphs"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="18151630" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/18151630/Infinite_state_games_with_finitary_conditions">Infinite-state games with finitary conditions</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="38114991" href="https://oxford.academia.edu/Nathana%C3%ABlFijalkow">Nathanaël Fijalkow</a></div><p class="ds-related-work--abstract ds2-5-body-sm">We study two-player zero-sum games over infinite-state graphs with boundedness conditions. Our first contribution is about the strategy complexity, i.e the memory required for winning strategies: we prove that over general infinite-state graphs, memoryless strategies are sufficient for finitary Büchi games, and finite-memory suffices for finitary parity games. We then study pushdown boundedness games, with two contributions. First we prove a collapse result for pushdown ωB games, implying the decidability of solving these games. Second we consider pushdown games with finitary parity along with stack boundedness conditions, and show that solving these games is EXPTIME-complete.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Infinite-state games with finitary conditions","attachmentId":39902721,"attachmentType":"pdf","work_url":"https://www.academia.edu/18151630/Infinite_state_games_with_finitary_conditions","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/18151630/Infinite_state_games_with_finitary_conditions"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="15589661" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/15589661/On_acyclicity_of_games_with_cycles">On acyclicity of games with cycles</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="34755661" href="https://business-rutgers.academia.edu/VladimirGurvich">Vladimir Gurvich</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Discrete Applied Mathematics, 2010</p><p class="ds-related-work--abstract ds2-5-body-sm">We study restricted improvement cycles (ri-cycles) in finite positional n-person games with perfect information modeled by directed graphs (digraphs) that may contain directed cycles (di-cycles). We obtain criteria of restricted improvement acyclicity (ri-acyclicity) in two cases: for n = 2 and for acyclic digraphs. We also provide several examples that outline the limits of these criteria and show that, essentially, there are no other ri-acyclic cases. We also discuss connections between ri-acyclicity and some open problems related to Nash-solvability.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On acyclicity of games with cycles","attachmentId":43057063,"attachmentType":"pdf","work_url":"https://www.academia.edu/15589661/On_acyclicity_of_games_with_cycles","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/15589661/On_acyclicity_of_games_with_cycles"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="2846847" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/2846847/Deterministic_graphical_games_revisited">Deterministic graphical games revisited</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="190602" href="https://au.academia.edu/KristofferArnsfeltHansen">Kristoffer Arnsfelt Hansen</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2012</p><p class="ds-related-work--abstract ds2-5-body-sm">Starting from Zermelo's classical formal treatment of chess, we trace through history the analysis of two-player win/lose/draw games with perfect information and potentially infinite play. Such chess-like games have appeared in many different research communities, and methods for solving them, such as retrograde analysis, have been rediscovered independently. We then revisit Washburn's deterministic graphical games (DGGs), a natural generalization of chess-like games to arbitrary zero-sum payoffs.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Deterministic graphical games revisited","attachmentId":30789948,"attachmentType":"pdf","work_url":"https://www.academia.edu/2846847/Deterministic_graphical_games_revisited","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/2846847/Deterministic_graphical_games_revisited"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":41164273,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":41164273,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_41164273" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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Björner</a></div><p class="ds-related-work--metadata ds2-5-body-xs">European Journal of Combinatorics, 1991</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Chip-firing Games on Graphs","attachmentId":89016998,"attachmentType":"pdf","work_url":"https://www.academia.edu/83782918/Chip_firing_Games_on_Graphs","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/83782918/Chip_firing_Games_on_Graphs"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="6" data-entity-id="18868260" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/18868260/Synchronic_Information_and_Common_Knowledge_in_Extensive_Games">Synchronic Information and Common Knowledge in Extensive Games</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="38421839" href="https://ucdavis.academia.edu/GiacomoBonanno">Giacomo Bonanno</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Synchronic Information and Common Knowledge in Extensive Games","attachmentId":40300196,"attachmentType":"pdf","work_url":"https://www.academia.edu/18868260/Synchronic_Information_and_Common_Knowledge_in_Extensive_Games","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/18868260/Synchronic_Information_and_Common_Knowledge_in_Extensive_Games"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="7" data-entity-id="124958831" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/124958831/The_Game_of_Arrows_on_3_Legged_Spider_Graphs">The Game of Arrows on 3-Legged Spider Graphs</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="322590076" href="https://independent.academia.edu/BryantMathews3">Bryant Mathews</a></div><p class="ds-related-work--metadata ds2-5-body-xs">arXiv (Cornell University), 2021</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The Game of Arrows on 3-Legged Spider Graphs","attachmentId":119087724,"attachmentType":"pdf","work_url":"https://www.academia.edu/124958831/The_Game_of_Arrows_on_3_Legged_Spider_Graphs","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/124958831/The_Game_of_Arrows_on_3_Legged_Spider_Graphs"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="8" data-entity-id="17574914" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/17574914/Games_on_graphs_and_sequentially_realizable_functionals_Extended_abstract">Games on graphs and sequentially realizable functionals. Extended abstract</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="37392216" href="https://cambridge.academia.edu/MartinHyland">Martin Hyland</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2002</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Games on graphs and sequentially realizable functionals. 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href="https://www.academia.edu/30624873/Game_theoretic_inductive_definability">Game-theoretic inductive definability</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="31477804" href="https://helsinki.academia.edu/JoukoVaananen">Jouko Väänänen</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Annals of Pure and Applied Logic, 1993</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Game-theoretic inductive definability","attachmentId":51072781,"attachmentType":"pdf","work_url":"https://www.academia.edu/30624873/Game_theoretic_inductive_definability","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a 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class="ds-related-work--metadata ds2-5-body-xs">1997</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Clusters of Two Player Games and Restricted Determinacy Theorem","attachmentId":100845154,"attachmentType":"pdf","work_url":"https://www.academia.edu/99871941/Clusters_of_Two_Player_Games_and_Restricted_Determinacy_Theorem","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/99871941/Clusters_of_Two_Player_Games_and_Restricted_Determinacy_Theorem"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" 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Kaiser</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Foundations of Software Science and …, 2010</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Degrees of Lookahead in Regular Infinite Games","attachmentId":7491809,"attachmentType":"pdf","work_url":"https://www.academia.edu/1011574/Degrees_of_Lookahead_in_Regular_Infinite_Games","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/1011574/Degrees_of_Lookahead_in_Regular_Infinite_Games"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" 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