Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Infinite games on finitely coloured graphs with applications to automata on infinite trees
Theoretical Computer Science
Small Progress Measures for Solving Parity Games
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
A Discrete Strategy Improvement Algorithm for Solving Parity Games
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
A deterministic subexponential algorithm for solving parity games
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Solving Parity Games in Practice
ATVA '09 Proceedings of the 7th International Symposium on Automated Technology for Verification and Analysis
An O(n2) time algorithm for alternating Büchi games
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
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We study a new form of attractor in parity games and use it to define solvers that run in PTIME and are partial in that they do not solve all games completely. Technically, for color c this new attractor determines whether player c% 2 can reach a set of nodes X of color c whilst avoiding any nodes of color less than c. Such an attractor is fatal if player c%2 can attract all nodes in X back to X in this manner. Our partial solvers detect fixed-points of nodes based on fatal attractors and correctly classify such nodes as won by player c%2. Experimental results show that our partial solvers completely solve benchmarks that were constructed to challenge existing full solvers. Our partial solvers also have encouraging run times in practice. For one partial solver we prove that its runtime is in $O({\mid\!{V}\!\mid}^3)$, that its output game is independent of the order in which attractors are computed, and that it solves all Büchi games.