{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article6532","name":"Banach-Mazur Games on Graphs","abstract":"We survey determinacy, definability, and \r\ncomplexity issues of Banach-Mazur games on finite and \r\ninfinite graphs.\r\n\r\nInfinite games where two players take turns to move a token \r\nthrough a directed graph, thus tracing out an infinite path, \r\nhave numerous applications in different branches of mathematics\r\nand computer science. In the usual format,\r\nthe possible moves of the players are given by\r\nthe edges of the graph; in each move\r\na player takes the token from its current position \r\nalong an edge to a next position. In Banach-Mazur games \r\nthe players instead select in each move a \\emph{path} \r\nof arbitrary finite length rather than just an edge. \r\nIn both cases the outcome of a play is an infinite \r\npath. A winning condition is thus given by a set of \r\ninfinite paths which is often specified by a logical formula,\r\nfor instance from S1S, LTL, or first-order logic. \r\n\r\nBanach-Mazur games have a long tradition in descriptive \r\nset theory and topology, and they have recently been shown to \r\nhave interesting applications also in computer science, \r\nfor instance for planning in nondeterministic domains,\r\nfor the study of fairness in concurrent systems, and\r\nfor the semantics of timed automata. \r\n\r\nIt turns out that Banach-Mazur games behave quite differently than \r\nthe usual graph games. Often they admit simpler winning strategies\r\nand more efficient algorithmic solutions. For instance, Banach-Mazur \r\ngames with $\\omega$-regular winning conditions always have \r\npositional winning strategies, and winning positions\r\nfor finite Banach-Mazur games with Muller winning condition\r\nare computable in polynomial time.","keywords":["Games","strategies","determinacy","positional determinacy","definability","complexity"],"author":{"@type":"Person","name":"Graedel, Erich","givenName":"Erich","familyName":"Graedel"},"position":15,"pageStart":364,"pageEnd":382,"dateCreated":"2008-12-05","datePublished":"2008-12-05","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/3.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Graedel, Erich","givenName":"Erich","familyName":"Graedel"},"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.FSTTCS.2008.1768","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6205","volumeNumber":2,"name":"IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science","dateCreated":"2008-12-05","datePublished":"2008-12-05","editor":[{"@type":"Person","name":"Hariharan, Ramesh","givenName":"Ramesh","familyName":"Hariharan"},{"@type":"Person","name":"Mukund, Madhavan","givenName":"Madhavan","familyName":"Mukund"},{"@type":"Person","name":"Vinay, V","givenName":"V","familyName":"Vinay"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article6532","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6205"}}}