Paper Info
Title
Solving parity games on integer vectors
Abstract
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.
Year
DOI
Venue
2013
10.1007/978-3-642-40184-8_9
international conference on concurrency theory
Keywords
DocType
Volume
integer vector,main result,parity game,integer counter,single-sided parity game,minimal element,multidimensional energy parity game,model checking vass,minimal initial credit,classic game problem
Conference
abs/1306.2806
Citations 
PageRank 
References 
15
0.75
26
Authors
4
Name
Order
Citations
PageRank
Parosh Aziz Abdulla12010122.22
Richard Mayr238922.29
Arnaud Sangnier323617.99
Jeremy Sproston472944.72