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
CONCUR '97 Proceedings of the 8th International Conference on Concurrency Theory
Efficient Büchi Automata from LTL Formulae
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Checking for Language Inclusion Using Simulation Preorders
CAV '91 Proceedings of the 3rd International Workshop on Computer Aided Verification
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
How much memory is needed to win infinite games?
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
A deterministic subexponential algorithm for solving parity games
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
From Nondeterministic Buchi and Streett Automata to Deterministic Parity Automata
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Faster Solutions of Rabin and Streett Games
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
On the complexity of omega -automata
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
The complexity of tree automata and logics of programs
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
An algebraic definition of simulation between programs
IJCAI'71 Proceedings of the 2nd international joint conference on Artificial intelligence
A hybrid algorithm for LTL games
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
Solving simple stochastic tail games
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Measuring permissiveness in parity games: mean-payoff parity games revisited
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
A survey of stochastic ω-regular games
Journal of Computer and System Sciences
Robustness in the presence of liveness
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
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We consider games where the winning conditions are disjunctions (or dually, conjunctions) of parity conditions; we call them generalized parity games. These winning conditions, while ω-regular, arise naturally when considering fair simulation between parity automata, secure equilibria for parity conditions, and determinization of Rabin automata. We show that these games retain the computational complexity of Rabin and Streett conditions; i.e., they are NP-complete and co-NP-complete, respectively. The (co-)NP-hardness is proved for the special case of a conjunction/disjunction of two parity conditions, which is the case that arises in fair simulation and secure equilibria. However, considering these games as Rabin or Streett games is not optimal. We give an exposition of Zielonka's algorithm when specialized to this kind of games. The complexity of solving these games for k parity objectives with d priorities, n states, and m edges is O(n2kd ċ m) ċ d!k/(kċd)!, as compared to O(n2kd ċm)ċ(kċd)!when these games are solved as Rabin/Streett games. We also extend the subexponential algorithm for solving parity games recently introduced by Jurdzinski, Paterson, and Zwick to generalized parity games. The resulting complexity of solving generalized parity games is nO(√n) ċ (kċd)/d!k. As a corollary we obtain an improved algorithm for Rabin and Streett games with d pairs, with time complexity nO(√n) ċ d!.