Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Computing with first-order logic
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Fixpoint logics, relational machines, and computational complexity
Journal of the ACM (JACM)
Infinite games on finitely coloured graphs with applications to automata on infinite trees
Theoretical Computer Science
The modal mu-calculus alternation hierarchy is strict
Theoretical Computer Science
Deciding the winner in parity games is in UP ∩ co-UP
Information Processing Letters
Bisimulation-invariant PTIME and higher-dimensional &mgr;-calculus
Theoretical Computer Science
Back and forth between guarded and modal logics
ACM Transactions on Computational Logic (TOCL)
Small Progress Measures for Solving Parity Games
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
The monadic second-order logic of graphs XIV: uniformly sparse graphs and edge set quantifications
Theoretical Computer Science
A deterministic subexponential algorithm for solving parity games
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
DAG-width: connectivity measure for directed graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Finite Model Theory and Its Applications (Texts in Theoretical Computer Science. An EATCS Series)
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STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Entanglement and the complexity of directed graphs
Theoretical Computer Science
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We study the logical definablity of the winning regions of parity games. For games with a bounded number of priorities, it is well-known that the winning regions are definable in the modal μ-calculus. Here we investigate the case of an unbounded number of priorities, both for finite game graphs and for arbitrary ones. In the general case, winning regions are definable in guarded second-order logic (GSO), but not in least-fixed point logic (LFP). On finite game graphs, winning regions are LFP-definable if, and only if, they are computable in polynomial time, and this result extends to any class of finite games that is closed under taking bisimulation quotients.