Solving Odd-Fair Parity Games

Authors Irmak Sağlam, Anne-Kathrin Schmuck



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Author Details

Irmak Sağlam
  • Max Planck Institute for Software Systems (MPI-SWS), Kaiserslautern, Germany
Anne-Kathrin Schmuck
  • Max Planck Institute for Software Systems (MPI-SWS), Kaiserslautern, Germany

Acknowledgements

We are grateful for the immense support provided by Munko Tsyrempilon for the experimental validation.

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Irmak Sağlam and Anne-Kathrin Schmuck. Solving Odd-Fair Parity Games. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 34:1-34:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.FSTTCS.2023.34

Abstract

This paper discusses the problem of efficiently solving parity games where player Odd has to obey an additional strong transition fairness constraint on its vertices - given that a player Odd vertex v is visited infinitely often, a particular subset of the outgoing edges (called live edges) of v has to be taken infinitely often. Such games, which we call Odd-fair parity games, naturally arise from abstractions of cyber-physical systems for planning and control. In this paper, we present a new Zielonka-type algorithm for solving Odd-fair parity games. This algorithm not only shares the same worst-case time complexity as Zielonka’s algorithm for (normal) parity games but also preserves the algorithmic advantage Zielonka’s algorithm possesses over other parity solvers with exponential time complexity. We additionally introduce a formalization of Odd player winning strategies in such games, which were unexplored previous to this work. This formalization serves dual purposes: firstly, it enables us to prove our Zielonka-type algorithm; secondly, it stands as a noteworthy contribution in its own right, augmenting our understanding of additional fairness assumptions in two-player games.

Subject Classification

ACM Subject Classification
  • Theory of computation → Solution concepts in game theory
Keywords
  • parity games
  • strong transition fairness
  • algorithmic game theory

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