Energy parity games are infinite two-player turn-based games played on weighted graphs. The objective of the game combines a (qualitative) parity condition with the (quantitative) requirement that the sum of the weights (i.e., the level of energy in the game) must remain positive. Beside their own

Abstract. Parity games are 2-player games of perfect information and infinite duration that have important applications in automata theory and decision procedures (validity as well as model checking) for temporal logics. In this paper we investigate practical aspects of solving parity games

Parity games are discrete infinite games of two players with complete information. There are two main motivations to study parity games. Firstly the problem of deciding a winner in a parity game is polynomially equivalent to the modal µ-calculus model checking, and therefore is very important

We study perfect-information stochastic parity games. These are two-player nonterminating games which are played on a graph with turn-based probabilistic transitions. A play results in an infinite path and the conflicting goals of the two players are!-regular path properties, formalized as parity

Abstract. Parity games are a powerful formalism for the automatic synthesis and verification of reactive systems. They are closely related to alternating ω-automata and emerge as a natural method for the solution of the µ-calculus model checking problem. Due to these strict connections, parity

Abstract. We study a class of parity games equipped with counters that evolve according to arbitrary non-negative affine functions. These games capture several cost models for dynamic systems from the literature. We present an elementary algorithm for computing the exact value of a counter parity

The question of the exact complexity of solving parity games is one of the major open problems in system verification, as it is equivalent to the problem of model-checking the modal µ-calculus. The known upper bound is NP∩co-NP, but no polynomial algorithm is known. It was shown that on tree

) constraints, then the corresponding objec-tive combines both a qualitative and a quantitative com-ponent. In a general case of interest, the qualitative com-ponent is a parity condition and the quantitative compo-nent is a mean-payoff reward. We study and solve such mean-payoff parity games. We also prove

to be useful in developing algorithms on directed graphs. In particular, we show that the problem of determining the winner of a parity game is solvable in polynomial time on graphs of bounded DAG-width. We also consider the relationship between DAG-width and other measures of such as entanglement and directed

Abstract. We present our GPU-based implementations of three well-known algorithms for solving parity games. Our implementations are in general faster by a factor of at least two than the corresponding imple-mentations found in the widely known PGSolver collection of solvers. For benchmarking we use