Document Zbl 0583.68020

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Comput. Syst. Sci.</a> <a href="/?q=in%3A151076" title="Articles in this Issue">31, 288-301 (1985)</a>. </div> <div class="abstract">We present a new characterization of PSPACE in terms of problems in a classical area in optimization, decision-making under uncertainty. These problems are modeled by certain games played against a disinterested opponent who makes moves at random. We show several natural problems of this sort to be PSPACE-complete.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A3934405">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A3934405">Cited in <strong>53</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A68Q25" title="MSC2020">68Q25</a> </td> <td class="space"> Analysis of algorithms and problem complexity </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A91A35" title="MSC2020">91A35</a> </td> <td class="space"> Decision theory for games </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A91A80" title="MSC2020">91A80</a> </td> <td class="space"> Applications of game theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3APSPACE">PSPACE</a>; <a href="/?q=ut%3Adecision-making+under+uncertainty">decision-making under uncertainty</a>; <a href="/?q=ut%3Agames+played+against+a+disinterested+opponent">games played against a disinterested opponent</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 0583.68020" data-ciurl="/ci/03934405" data-biburl="/bibtex/03934405.bib" data-amsurl="/amsrefs/03934405.bib" data-xmlurl="/xml/03934405.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/03934405.pdf" title="Zbl 0583.68020 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/0022-0000(85)90045-5" aria-label="DOI for “Games against nature”" title="10.1016/0022-0000(85)90045-5">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Bertsekas, D., Dynamic Programming and Stochastic Control (1976), Academic Press: Academic Press New York · <a href="/0549.93064" class="nowrap">Zbl 0549.93064</a></td> </tr><tr> <td>[2]</td> <td class="space">Chandra, A.; Stockmeyer, L. J., Alternation, (Proc. 17th Found. of Comput. Sci. (1976)) · <a href="/0473.68043" class="nowrap">Zbl 0473.68043</a></td> </tr><tr> <td>[3]</td> <td class="space"><span class="zbmathjax-textsc">M. Chandy and J. Robinson</span>, unpublished manuscript, University of Texas, Austin, 1982.; <span class="zbmathjax-textsc">M. Chandy and J. Robinson</span>, unpublished manuscript, University of Texas, Austin, 1982.</td> </tr><tr> <td>[4]</td> <td class="space">Cook, S. A., The complexity of theorem proving procedures, (Proc. 3rd ACM Symposium on the Theory of Computing (1971)), 151-158 · <a href="/0363.68125" class="nowrap">Zbl 0363.68125</a></td> </tr><tr> <td>[5]</td> <td class="space">Denardo, E., Dynamic Programming: Models and Applications (1982), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J · <a href="/1029.90075" class="nowrap">Zbl 1029.90075</a></td> </tr><tr> <td>[6]</td> <td class="space">Derman, C., Finite State Markov Decision Processes (1972), Academic Press: Academic Press New York</td> </tr><tr> <td>[7]</td> <td class="space">Garey, M. R.; Johnson, D. S., Computers and Intractability: A Guide to the Theory of NP-completeness (1979), Freeman: Freeman San Francisco · <a href="/0411.68039" class="nowrap">Zbl 0411.68039</a></td> </tr><tr> <td>[8]</td> <td class="space">Garey, M. R.; Johnson, D. S.; Tarjan, R. E., The planar Hamilton circuit problem is NP-complete, SIAM J. Comput., 5, 704-714 (1976) · <a href="/0346.05110" class="nowrap">Zbl 0346.05110</a></td> </tr><tr> <td>[9]</td> <td class="space">Gill, J., The computational complexity of probabilistic Turing machines, SIAM J. Comput., 6, 675-695 (1977) · <a href="/0366.02024" class="nowrap">Zbl 0366.02024</a></td> </tr><tr> <td>[10]</td> <td class="space">Howard, R., Dynamic Programming and Markov Processes (1960), MIT Press: MIT Press Cambridge, Mass · <a href="/0091.16001" class="nowrap">Zbl 0091.16001</a></td> </tr><tr> <td>[11]</td> <td class="space">Orlin, J., The complexity of periodic of periodic problems, (Proc. 21st ACM Sympos. Theory of Comput. (1980))</td> </tr><tr> <td>[12]</td> <td class="space">Papadimitriou, C. H.; Steiglitz, K., Combinatorial Optimization: Algorithms and Complexity (1982), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J · <a href="/0503.90060" class="nowrap">Zbl 0503.90060</a></td> </tr><tr> <td>[13]</td> <td class="space">Reie, J., Logics for probabilistic programming, (Proc. 12th ACM Sympos. Theory of Comput. (1980))</td> </tr><tr> <td>[14]</td> <td class="space">Schaefer, T. J., The complexity of some two-person perfect-information games, J. Comput. System Sci., 16, 185-225 (1978) · <a href="/0383.90112" class="nowrap">Zbl 0383.90112</a></td> </tr><tr> <td>[15]</td> <td class="space">Stockmeyer, L. J., The polynomial time hierarchy, Theor. Comput. Sci., 1, 1-22 (1976) · <a href="/0353.02024" class="nowrap">Zbl 0353.02024</a></td> </tr><tr> <td>[16]</td> <td class="space">Valiant, L. G., The complexity of computing the permanent, Theor. Comput. Sci., 00 (1979) · <a href="/0415.68008" class="nowrap">Zbl 0415.68008</a></td> </tr><tr> <td>[17]</td> <td class="space">(Coffman, E. G., Computer and Job-shop Scheduling Theory (1976), Wiley: Wiley New York) · <a href="/0359.90031" class="nowrap">Zbl 0359.90031</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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