Cyclic games and an algorithm to find minimax cycle means in directed graphs
USSR Computational Mathematics and Mathematical Physics
The complexity of mean payoff games on graphs
Theoretical Computer Science
Deciding the winner in parity games is in UP ∩ co-UP
Information Processing Letters
Total reward stochastic games and sensitive average reward strategies
Journal of Optimization Theory and Applications
Mathematics of Operations Research
Quantitative stochastic parity games
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A combinatorial strongly subexponential strategy improvement algorithm for mean payoff games
Discrete Applied Mathematics
Reduction of stochastic parity to stochastic mean-payoff games
Information Processing Letters
Probabilistic Systems with LimSup and LimInf Objectives
Infinity in Logic and Computation
Computing game values for crash games
ATVA'07 Proceedings of the 5th international conference on Automated technology for verification and analysis
Strategy improvement and randomized subexponential algorithms for stochastic parity games
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
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In this paper we consider two-player zero-sum payoff games on finite graphs, both in the deterministic as well as in the stochastic setting. In the deterministic setting, we consider total-payoff games which have been introduced as a refinement of mean-payoff games [10, 18]. In the stochastic setting, our class is a turn-based variant of liminf-payoff games [4, 15, 16]. In both settings, we provide a non-trivial characterization of the values through nested fixpoint equations. The characterization of the values of liminf-payoff games moreover shows that solving liminf-payoff games is polynomial-time reducible to solving stochastic parity games. We construct practical algorithms for solving the occurring nested fixpoint equations based on strategy iteration. As a corollary we obtain that solving deterministic total-payoff games and solving stochastic liminf-payoff games is in UP *** co*** UP.