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Parity and Exploration Games on Infinite Graphs

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Computer Science Logic (CSL 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3210))

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Abstract

This paper examines two players’ turn-based perfect-information games played on infinite graphs. Our attention is focused on the classes of games where winning conditions are boolean combinations of the following two conditions: (1) the first one states that an infinite play is won by player 0 if during the play infinitely many different vertices were visited, (2) the second one is the well known parity condition generalized to a countable number of priorities.

We show that, in most cases, both players have positional winning strategies and we characterize their respective winning sets. In the special case of pushdown graphs, we use these results to show that the sets of winning positions are regular and we show how to compute them as well as positional winning strategies in exponential time.

This research was supported by European Research Training Network: Games and Automata for Synthesis and Validation.

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Author information

Authors and Affiliations

  1. Université Paris 7, LIAFA, case 7014, 2, place Jussieu, 75251 Cedex 05, Paris, France

    Hugo Gimbert

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  1. Hugo Gimbert
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Editor information

Editors and Affiliations

  1. Wroclaw University, Poland

    Jerzy Marcinkowski

  2. Polish Academy of Sciences, Institute of Computer Science, Poland

    Andrzej Tarlecki

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Gimbert, H. (2004). Parity and Exploration Games on Infinite Graphs. In: Marcinkowski, J., Tarlecki, A. (eds) Computer Science Logic. CSL 2004. Lecture Notes in Computer Science, vol 3210. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30124-0_8

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  • DOI: https://doi.org/10.1007/978-3-540-30124-0_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23024-3

  • Online ISBN: 978-3-540-30124-0

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