Supervisory control of a class of discrete event processes
SIAM Journal on Control and Optimization
On the synthesis of a reactive module
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The temporal logic of reactive and concurrent systems
The temporal logic of reactive and concurrent systems
The complexity of stochastic games
Information and Computation
Competitive Markov decision processes
Competitive Markov decision processes
Languages, automata, and logic
Handbook of formal languages, vol. 3
Games, Probability, and the Quantitative µ-Calculus qMµ
LPAR '02 Proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Quantitative stochastic parity games
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The complexity of tree automata and logics of programs
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Code aware resource management
Proceedings of the 5th ACM international conference on Embedded software
Information Processing Letters
Games, Time, and Probability: Graph Models for System Design and Analysis
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
Optimal strategy synthesis in stochastic Müller games
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
On reachability games of ordinal length
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Information and Computation
Decision problems for Nash equilibria in stochastic games
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Solving simple stochastic tail games
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Qualitative reachability in stochastic BPA games
Information and Computation
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Strategy improvement and randomized subexponential algorithms for stochastic parity games
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
A survey of stochastic ω-regular games
Journal of Computer and System Sciences
The complexity of stochastic Müller games
Information and Computation
Strategy improvement for stochastic rabin and streett games
CONCUR'06 Proceedings of the 17th international conference on Concurrency Theory
Strategy synthesis for markov decision processes and branching-time logics
CONCUR'07 Proceedings of the 18th international conference on Concurrency Theory
Towards communication-based steering of complex distributed systems
Proceedings of the 17th Monterey conference on Large-Scale Complex IT Systems: development, operation and management
Code aware resource management
Formal Methods in System Design
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The theory of graph games with ω-regular winning conditions is the foundation for modeling and synthesizing reactive processes. In the case of stochastic reactive processes, the corresponding stochastic graph games have three players, two of them (System and Environment) behaving adversarially, and the third (Uncertainty) behaving probabilistically. We consider two problems for stochastic graph games: the qualitative problem asks for the set of states from which a player can win with probability 1 (almost-sure winning); the quantitative problem asks for the maximal probability of winning (optimal winning) from each state. We show that for Rabin winning conditions, both problems are in NP. As these problems were known to be NP-hard, it follows that they are NP-complete for Rabin conditions, and dually, coNP-complete for Streett conditions. The proof proceeds by showing that pure memoryless strategies suffice for qualitatively and quantitatively winning stochastic graph games with Rabin conditions. This insight is of interest in its own right, as it implies that controllers for Rabin objectives have simple implementations. We also prove that for every ω-regular condition, optimal winning strategies are no more complex than almost-sure winning strategies.