The complexity of stochastic games
Information and Computation
On the complexity of the parity argument and other inefficient proofs of existence
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
The complexity of mean payoff games on graphs
Theoretical Computer Science
Competitive Markov decision processes
Competitive Markov decision processes
Deciding the winner in parity games is in UP ∩ co-UP
Information Processing Letters
A Discrete Subexponential Algorithm for Parity Games
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of 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
On Model-Checking for Fragments of µ-Calculus
CAV '93 Proceedings of the 5th International Conference on Computer Aided Verification
Automata logics, and infinite games: a guide to current research
Automata logics, and infinite games: a guide to current research
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
A Simple P-Matrix Linear Complementarity Problem for Discounted Games
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
A Deterministic Subexponential Algorithm for Solving Parity Games
SIAM Journal on Computing
Linear complementarity and p-matrices for stochastic games
PSI'06 Proceedings of the 6th international Andrei Ershov memorial conference on Perspectives of systems informatics
Solving parity games in big steps
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Simple stochastic games and p-matrix generalized linear complementarity problems
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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Solving parity games is an algorithmic problem which is polynomial-time equivalent to the modal mu-calculus model checking problem [5], and hence of fundamental importance for the automated verification of computational systems [8]. Establishing its exact computational complexity is an intriguing long-standing open problem. The problem is known to be in UP (unambiguous NP) and co- UP [9], but no polynomial time algorithm or complexity-theoretic evidence of hardness have been found, since almost two decades ago when its membership to NP and co-NP was exhibited [5].