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
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Reasoning about infinite computations
Information and Computation
Probabilistic predicate transformers
ACM Transactions on Programming Languages and Systems (TOPLAS)
Competitive Markov decision processes
Competitive Markov decision processes
Model Checking of Probabalistic and Nondeterministic Systems
Proceedings of the 15th Conference on Foundations of Software Technology and Theoretical Computer Science
It Usually Works: The Temporal Logic of Stochastic Systems
Proceedings of the 7th International Conference on Computer Aided Verification
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
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of 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
A deterministic subexponential algorithm for solving parity games
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The complexity of quantitative concurrent parity games
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Results on the quantitative μ-calculus qMμ
ACM Transactions on Computational Logic (TOCL)
Theoretical Computer Science
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
25 Years of Model Checking
Automata, Probability, and Recursion
CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
Termination criteria for solving concurrent safety and reachability games
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Model checking nash equilibria in MAD distributed systems
Proceedings of the 2008 International Conference on Formal Methods in Computer-Aided Design
A Novel Stochastic Game Via the Quantitative μ-calculus
Electronic Notes in Theoretical Computer Science (ENTCS)
Magnifying-lens abstraction for Markov decision processes
CAV'07 Proceedings of the 19th international conference on Computer aided verification
Qualitative concurrent parity games
ACM Transactions on Computational Logic (TOCL)
Probabilistic modal µ-calculus with independent product
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Qualitative reachability in stochastic BPA games
Information and Computation
Recursive concurrent stochastic games
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Verifying quantitative properties using bound functions
CHARME'05 Proceedings of the 13 IFIP WG 10.5 international conference on Correct Hardware Design and Verification Methods
Analysis of recursive probabilistic models
ATVA'06 Proceedings of the 4th international conference on Automated Technology for Verification and Analysis
Simulation-Based graph similarity
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
An algorithm for probabilistic alternating simulation
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Computing game metrics on markov decision processes
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Perfect information stochastic priority games
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Strategy improvement for concurrent reachability and turn-based stochastic safety games
Journal of Computer and System Sciences
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We consider two-player games played for an infinite number of rounds, with ω-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 µ-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 ω-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 ε-optimal, is only guaranteed in games with safety winning conditions.