Probabilistic propositional temporal logics
Information and Control
Temporal reasoning under generalized fairness constraints
3rd annual symposium on theoretical aspects of computer science on STACS 86
On the synthesis of a reactive module
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Bisimulation through probabilistic testing
Information and Computation
Model checking and abstraction
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The complexity of stochastic games
Information and Computation
Reasoning about infinite computations
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The complexity of probabilistic verification
Journal of the ACM (JACM)
Modalities for model checking (extended abstract): branching time strikes back
POPL '85 Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
An automata-theoretic approach to branching-time model checking
Journal of the ACM (JACM)
Information and Computation
Termination of probabilistic concurrent programs: (extended abstract)
POPL '82 Proceedings of the 9th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
CTL+ is Exponentially more Succinct than CTL
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
State Space Reductions for Alternating Büchi Automata
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
It Usually Works: The Temporal Logic of Stochastic Systems
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SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The Existence of Finite Abstractions for Branching Time Model Checking
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LiQuor: A tool for Qualitative and Quantitative Linear Time analysis of Reactive Systems
QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
Game-based Abstraction for Markov Decision Processes
QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
The Satisfiability Problem for Probabilistic CTL
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
Automatic verification of probabilistic concurrent finite state programs
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Automata and fixed point logic: A coalgebraic perspective
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
PCTL model checking of Markov chains: Truth and falsity as winning strategies in games
Performance Evaluation
Compositional Design Methodology with Constraint Markov Chains
QEST '10 Proceedings of the 2010 Seventh International Conference on the Quantitative Evaluation of Systems
p-Automata: New Foundations for Discrete-Time Probabilistic Verification
QEST '10 Proceedings of the 2010 Seventh International Conference on the Quantitative Evaluation of Systems
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
PRISM: a tool for automatic verification of probabilistic systems
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Don’t know in probabilistic systems
SPIN'06 Proceedings of the 13th international conference on Model Checking Software
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We introduce p-Automata, which are automata that accept languages of Markov chains, by adapting notions and techniques from alternating tree automata to the realm of Markov chains. The set of languages of p-automata is closed under Boolean operations, and for every PCTL formula it contains the language of the set of models of the formula. Furthermore, the language of every p-automaton is closed under probabilistic bisimulation. Similar to tree automata, whose acceptance is defined via two-player games, we define acceptance of Markov chains by p-automata through two-player stochastic games. We show that acceptance is solvable in EXPTIME; but for automata that arise from PCTL formulas acceptance matches that of PCTL model checking, namely, linear in the formula and polynomial in the Markov chain. We also derive a notion of simulation between p-automata that approximates language containment in EXPTIME and is complete for Markov chains. These foundations therefore enable abstraction-based probabilistic model checking for probabilistic specifications that subsume Markov chains, and LTL and CTL* like logics.