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

Matthew Hague, Roland Meyer, Sebastian Muskalla, Martin Zimmermann

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.
Original languageEnglish
Title of host publicationInternational Symposium of Mathematical Foundations of Computer Science
Number of pages15
Publication statusPublished - 20 Aug 2018

Publication series

NameLeibniz International Proceedings in Informatics (LIPIcs)


  • Parity Games, Safety Games, Pushdown Systems, Collapsible Pushdown Systems, Higher-Order Recursion Schemes, Model Checking

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