Markov decision processes and regular events
Proceedings of the seventeenth international colloquium on Automata, languages and programming
Handbook of theoretical computer science (vol. B)
Abstract interpretation and application to logic programs
Journal of Logic Programming
Modeling and verification of randomized distributed real-time systems
Modeling and verification of randomized distributed real-time systems
Model checking
An abstract Monte-Carlo method for the analysis of probabilistic programs
POPL '01 Proceedings of the 28th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Quantitative solution of omega-regular games380872
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Testing Preorders for Probabilistic Processes
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
Symbolic Model Checking for Probabilistic Processes
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Abstraction of Expectation Functions Using Gaussian Distributions
VMCAI 2003 Proceedings of the 4th International Conference on Verification, Model Checking, and Abstract Interpretation
Model Checking of Probabalistic and Nondeterministic Systems
Proceedings of the 15th Conference on Foundations of Software Technology and Theoretical Computer Science
Abstract Interpretation of Probabilistic Semantics
SAS '00 Proceedings of the 7th International Symposium on Static Analysis
Efficient dynamic-programming updates in partially observable Markov decision processes
Efficient dynamic-programming updates in partially observable Markov decision processes
A logic for reasoning about time and reability
A logic for reasoning about time and reability
Formal verification of probabilistic systems
Formal verification of probabilistic systems
On finite-state approximants for probabilistic computation tree logic
Theoretical Computer Science - Quantitative aspects of programming languages (QAPL 2004)
Probabilistic abstractions with arbitrary domains
SAS'11 Proceedings of the 18th international conference on Static analysis
Modeling, optimization and computation for software verification
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
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We propose a formal language for the specification of trace properties of probabilistic, nondeterministic transition systems, encompassing the properties expressible in Linear Time Logic. Those formulas are in general undecidable on infinite deterministic transition systems and thus on infinite Markov decision processes. This language has both a semantics in terms of sets of traces, as well as another semantics in terms of measurable functions; we give and prove theorems linking the two semantics. We then apply abstract interpretation-based techniques to give upper bounds on the worst-case probability of the studied property. We propose an enhancement of this technique when the state space is partitioned -- for instance along the program points --, allowing the use of faster iteration methods.