Solving Parity Games on Integer Vectors

Parosh Aziz Abdulla, Richard Mayr, Arnaud Sangnier, Jeremy Sproston

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


We consider parity games on infinite graphs where configurations are represented by control-states and integer vectors. This framework subsumes two classic game problems: parity games on vector addition systems with states (vass) and multidimensional energy parity games. We show that the multidimensional energy parity game problem is inter-reducible with a subclass of single-sided parity games on vass where just one player can modify the integer counters and the opponent can only change control-states. Our main result is that the minimal elements of the upward-closed winning set of these single-sided parity games on vass are computable. This implies that the Pareto frontier of the minimal initial credit needed to win multidimensional energy parity games is also computable, solving an open question from the literature. Moreover, our main result implies the decidability of weak simulation preorder/equivalence between finite-state systems and vass, and the decidability of model checking vass with a large fragment of the modal μ-calculus.
Original languageEnglish
Title of host publicationCONCUR 2013 - Concurrency Theory
Subtitle of host publication 24th International Conference, CONCUR 2013, Buenos Aires, Argentina, August 27-30, 2013. Proceedings
PublisherSpringer Berlin Heidelberg
Number of pages15
ISBN (Electronic)978-3-642-40184-8
ISBN (Print)978-3-642-40183-1
Publication statusPublished - 2013


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