Markov decision processes and regular events
Proceedings of the seventeenth international colloquium on Automata, languages and programming
Sequential circuit verification using symbolic model checking
DAC '90 Proceedings of the 27th ACM/IEEE Design Automation Conference
Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
The temporal logic of reactive and concurrent systems
The temporal logic of reactive and concurrent systems
Probabilistic predicate transformers
ACM Transactions on Programming Languages and Systems (TOPLAS)
Competitive Markov decision processes
Competitive Markov decision processes
Dynamic Programming and Optimal Control
Dynamic Programming and Optimal Control
Quantitative Analysis and Model Checking
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Concurrent Omega-Regular Games
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Games, Probability, and the Quantitative µ-Calculus qMµ
LPAR '02 Proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Quantitative stochastic parity games
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Two-player nonzero-sum ω-regular games
CONCUR 2005 - Concurrency Theory
Abstract interpretation of programs as Markov decision processes
Science of Computer Programming - Special issue: Static analysis symposium (SAS 2003)
Concurrent games with tail objectives
Theoretical Computer Science
Discounting Infinite Games But How and Why?
Electronic Notes in Theoretical Computer Science (ENTCS)
New Algorithms for Solving Simple Stochastic Games
Electronic Notes in Theoretical Computer Science (ENTCS)
Discounting the future in systems theory
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Abstract interpretation of programs as Markov decision processes
SAS'03 Proceedings of the 10th international conference on Static analysis
Multi-valued model checking games
ATVA'05 Proceedings of the Third international conference on Automated Technology for Verification and Analysis
A survey of stochastic ω-regular games
Journal of Computer and System Sciences
Multi-valued model checking games
Journal of Computer and System Sciences
Concurrent games with tail objectives
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
A game based model of security for key predistribution schemes in wireless sensor network
ICDCIT'05 Proceedings of the Second international conference on Distributed Computing and Internet Technology
Robustness of structurally equivalent concurrent parity games
FOSSACS'12 Proceedings of the 15th international conference on Foundations of Software Science and Computational Structures
Equivalence of games with probabilistic uncertainty and partial-observation games
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
Towards communication-based steering of complex distributed systems
Proceedings of the 17th Monterey conference on Large-Scale Complex IT Systems: development, operation and management
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We consider two-player games played for an infinite number of rounds, with &ohgr;-regular winning conditions. The games may be concurrent, in that the players choose their moves simultaneously and independently, and probabilistic, in that the moves determine a probability distribution for the successor state. We introduce quantitative game &mgr;-calculus, and we show that the maximal probability of winning such games can be expressed as the fixpoint formulas in this calculus. We develop the arguments both for deterministic and for probabilistic concurrent games; as a special case, we solve probabilistic turn-based games with &ohgr;-regular winning conditions, which was also open. We also characterize the optimality, and the memory requirements, of the winning strategies. In particular, we show that while memoryless strategies suffice for winning games with safety and reachability conditions, Büchi conditions require the use of strategies with infinite memory. The existence of optimal strategies, as opposed to &egr;-optimal, is only guaranteed in games with safety winning conditions.