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Admissible Strategies in Infinite Games over Graphs

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Mathematical Foundations of Computer Science 2009 (MFCS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5734))

Abstract

We consider games played on finite graphs, whose objective is to obtain a trace belonging to a given set of accepting traces. We focus on the states from which Player 1 cannot force a win. We compare several criteria for establishing what is the preferable behavior of Player 1 from those states, eventually settling on the notion of admissible strategy.

As the main result, we provide a characterization of the goals admitting positional admissible strategies. In addition, we derive a simple algorithm for computing such strategies for various common goals, and we prove the equivalence between the existence of positional winning strategies and the existence of positional subgame perfect strategies.

This work was supported by the MIUR PRIN Project 2007-9E5KM8.

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Author information

Authors and Affiliations

  1. Università di Napoli “Federico II”, Italy

    Marco Faella

Authors
  1. Marco Faella
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Faculty of Mathematics, Physics and Informatics, Comenius University, Research partially funded by grant APVV 0433-06, Bratislava, Slovakia

    Rastislav Královič

  2. Members of EACSL Jury for the Ackermann Award, Poland

    Damian Niwiński

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Faella, M. (2009). Admissible Strategies in Infinite Games over Graphs. In: Královič, R., Niwiński, D. (eds) Mathematical Foundations of Computer Science 2009. MFCS 2009. Lecture Notes in Computer Science, vol 5734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03816-7_27

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  • DOI: https://doi.org/10.1007/978-3-642-03816-7_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03815-0

  • Online ISBN: 978-3-642-03816-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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