The complexity of stochastic games
Information and Computation
Model-checking in dense real-time
Information and Computation - Special issue: selections from 1990 IEEE symposium on logic in computer science
Theoretical Computer Science
Symbolic model checking for real-time systems
Information and Computation
The complexity of probabilistic verification
Journal of the ACM (JACM)
Competitive Markov decision processes
Competitive Markov decision processes
Model checking
Alternating-time temporal logic
Journal of the ACM (JACM)
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
Automata logics, and infinite games: a guide to current research
Automata logics, and infinite games: a guide to current research
Quantitative stochastic parity games
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Quantitative solution of omega-regular games
Journal of Computer and System Sciences - STOC 2001
The complexity of quantitative concurrent parity games
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Strategy Improvement for Concurrent Reachability Games
QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
Strategy improvement and randomized subexponential algorithms for stochastic parity games
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
The complexity of stochastic rabin and streett games
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Timed alternating-time temporal logic
FORMATS'06 Proceedings of the 4th international conference on Formal Modeling and Analysis of Timed Systems
Strategy improvement for stochastic rabin and streett games
CONCUR'06 Proceedings of the 17th international conference on Concurrency Theory
Theory and Practice of Probabilistic Timed Game for Embedded Systems
ICESS '07 Proceedings of the 3rd international conference on Embedded Software and Systems
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Digital technology is increasingly deployed in safety-critical situations. This calls for systematic design and verification methodologies that can cope with three major sources of system complexity: concurrency, real time, and uncertainty. We advocate a two-step process: formal modeling followed by algorithmic analysis (or, "model building" followed by "model checking"). We model the concurrent components of a reactive system as potential collaborators or adversaries in a multi-player game with temporal objectives, such as system safety. The real-time aspect of embedded systems requires models that combine discrete state transitions and continuous state evolutions. Uncertainty in the environment is naturally modeled by probabilistic state changes. As a result, we obtain three orthogonal extensions of the basic state-transition graph model for reactive systems --game graphs, timed graphs, and stochastic graphs-- as well as combinations thereof. In this short text, we provide a uniform exposition of the underlying definitions. For verification algorithms, we refer the reader to the literature.