Parity to Safety in Polynomial Time for Pushdown and Collapsible Pushdown Systems

Authors Matthew Hague , Roland Meyer, Sebastian Muskalla , Martin Zimmermann

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Author Details

Matthew Hague
  • Royal Holloway, University of London, UK
Roland Meyer
  • TU Braunschweig, Germany
Sebastian Muskalla
  • TU Braunschweig, Germany
Martin Zimmermann
  • Universität des Saarlandes, Saarbrücken, Germany

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Matthew Hague, Roland Meyer, Sebastian Muskalla, and Martin Zimmermann. Parity to Safety in Polynomial Time for Pushdown and Collapsible Pushdown Systems. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 57:1-57:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We give a direct polynomial-time reduction from parity games played over the configuration graphs of collapsible pushdown systems to safety games played over the same class of graphs. That a polynomial-time reduction would exist was known since both problems are complete for the same complexity class. Coming up with a direct reduction, however, has been an open problem. Our solution to the puzzle brings together a number of techniques for pushdown games and adds three new ones. This work contributes to a recent trend of liveness to safety reductions which allow the advanced state-of-the-art in safety checking to be used for more expressive specifications.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Theory of computation → Modal and temporal logics
  • Theory of computation → Verification by model checking
  • Theory of computation → Grammars and context-free languages
  • Parity Games
  • Safety Games
  • Pushdown Systems
  • Collapsible Pushdown Systems
  • Higher-Order Recursion Schemes
  • Model Checking


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