Bisimulation through probabilistic testing (preliminary report)
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Probabilistic Lossy Channel Systems
TAPSOFT '97 Proceedings of the 7th International Joint Conference CAAP/FASE on Theory and Practice of Software Development
Probabilistic Simulations for Probabilistic Processes
CONCUR '94 Proceedings of the Concurrency Theory
Bisimulation for labelled Markov processes
Information and Computation - Special issue: LICS'97
Approximating labelled Markov processes
Information and Computation
Results on the quantitative μ-calculus qMμ
ACM Transactions on Computational Logic (TOCL)
Hintikka Games for PCTL on Labeled Markov Chains
QEST '08 Proceedings of the 2008 Fifth International Conference on Quantitative Evaluation of Systems
Quantitative analysis of probabilistic lossy channel systems
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Counterexamples in probabilistic model checking
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
Three-valued abstractions of Markov chains: completeness for a sizeable fragment of PCTL
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
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
Minimal critical subsystems for discrete-time markov models
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
p-Automata: New foundations for discrete-time probabilistic verification
Performance Evaluation
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Probabilistic model checking is a technique for verifying whether a model such as a Markov chain satisfies a probabilistic, behavioral property-e.g. ''with probability at least 0.999, a device will be elected leader''. Such properties are expressible in probabilistic temporal logics, e.g. PCTL, and efficient algorithms exist for checking whether these formulae are true or false on finite-state models. Alas, these algorithms do not supply diagnostic information for why a probabilistic property does or does not hold in a given model. We provide here complete and rigorous foundations for such diagnostics in the setting of countable labeled Markov chains and PCTL. For each model and PCTL formula, we define a game between a Verifier and a Refuter that is won by Verifier if the formula holds in the model, and won by Refuter if it does not hold. Games are won by exactly one player, through monotone strategies that encode the diagnostic information for truth and falsity (respectively). These games are infinite with Buchi type acceptance conditions where simpler fairness conditions are shown to be not sufficient. Verifier can always force finite plays for certain PCTL formulae, suggesting the existence of finite-state abstractions of models that satisfy such formulae.