A Technique to Speed up Symmetric Attractor-Based Algorithms for Parity Games

Authors K. S. Thejaswini, Pierre Ohlmann, Marcin Jurdziński

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K. S. Thejaswini
  • Department of Computer Science, University of Warwick, Coventry, UK
Pierre Ohlmann
  • University of Warsaw, Poland
Marcin Jurdziński
  • Department of Computer Science, University of Warwick, Coventry, UK


We thank Rémi Morvan for contributing to several simulating discussions. We are grateful to Aditya Prakash for proof reading the current version of the paper, and to Nathanaël Fijalkow and Olivier Serre for doing the same with an earlier version of the paper. We also thank anonymous referees for pointing out some missing references from our previous draft as well as for their valuable comments to improve our current presentation. The authors are listed in reverse alphabetical order.

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K. S. Thejaswini, Pierre Ohlmann, and Marcin Jurdziński. A Technique to Speed up Symmetric Attractor-Based Algorithms for Parity Games. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 44:1-44:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


The classic McNaughton-Zielonka algorithm for solving parity games has excellent performance in practice, but its worst-case asymptotic complexity is worse than that of the state-of-the-art algorithms. This work pinpoints the mechanism that is responsible for this relative underperformance and proposes a new technique that eliminates it. The culprit is the wasteful manner in which the results obtained from recursive calls are indiscriminately discarded by the algorithm whenever subgames on which the algorithm is run change. Our new technique is based on firstly enhancing the algorithm to compute attractor decompositions of subgames instead of just winning strategies on them, and then on making it carefully use attractor decompositions computed in prior recursive calls to reduce the size of subgames on which further recursive calls are made. We illustrate the new technique on the classic example of the recursive McNaughton-Zielonka algorithm, but it can be applied to other symmetric attractor-based algorithms that were inspired by it, such as the quasi-polynomial versions of the McNaughton-Zielonka algorithm based on universal trees.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Logic and verification
  • Parity games
  • Attractor decomposition
  • Quasipolynomial Algorithms
  • Universal trees


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