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Jumping Automata for Uniform Strategies

Authors Bastien Maubert, Sophie Pinchinat



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Bastien Maubert
Sophie Pinchinat

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Bastien Maubert and Sophie Pinchinat. Jumping Automata for Uniform Strategies. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 287-298, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)
https://doi.org/10.4230/LIPIcs.FSTTCS.2013.287

Abstract

The concept of uniform strategies has recently been proposed as a relevant notion in game theory for computer science. It relies on properties involving sets of plays in two-player turn-based arenas equipped with a binary relation between plays. Among the two notions of fully-uniform and strictly-uniform strategies, we focus on the latter, less explored. We present a language that extends CTL^* with a quantifier over all related plays, which enables to express a rich class of uniformity constraints on strategies. We show that the existence of a uniform strategy is equivalent to the language non-emptiness of a jumping tree automaton. While the existence of a uniform strategy is undecidable for rational binary relations, restricting to ecognizable relations yields a 2EXPTIME-complete complexity, and still captures a class of two-player imperfect-information games with epistemic temporal objectives. This result relies on a translation from jumping tree automata with recognizable relations to two-way tree automata.
Keywords
  • Games
  • Imperfect information
  • Uniform strategies
  • Jumping automata

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