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

05/08/2018

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by   Matthew Hague, et al.

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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 by complexity theory. 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.