Theoretical Computer Science
Modeling and verification of randomized distributed real-time systems
Modeling and verification of randomized distributed real-time systems
Modal and temporal properties of processes
Modal and temporal properties of processes
Quantitative Analysis and Model Checking
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Results on the quantitative μ-calculus qMμ
ACM Transactions on Computational Logic (TOCL)
Principles of Model Checking (Representation and Mind Series)
Principles of Model Checking (Representation and Mind Series)
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Stochastic o-regular games
Labelled Markov Processes
Abstract probabilistic automata
VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
Quantitative multi-objective verification for probabilistic systems
TACAS'11/ETAPS'11 Proceedings of the 17th international conference on Tools and algorithms for the construction and analysis of systems: part of the joint European conferences on theory and practice of software
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Sequent calculi for induction and infinite descent
Journal of Logic and Computation
The embedded systems design challenge
FM'06 Proceedings of the 14th international conference on Formal Methods
Assume-Guarantee verification for probabilistic systems
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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We present a formal proof system for compositional verification of probabilistic concurrent processes. Processes are specified using an SOS-style process algebra with probabilistic operators. Properties are expressed using a probabilistic modal μ-calculus. And the proof system is formulated as a sequent calculus in which sequents are given a quantitative interpretation. A key feature is that the probabilistic scenario is handled by introducing the notion of Markov proof, according to which proof trees contain probabilistic branches and are required to satisfy a condition formulated by interpreting them as Markov Decision Processes. We present simple but illustrative examples demonstrating the applicability of the approach to the compositional verification of infinite state processes. Our main result is the soundness of the proof system, which is proved by applying the coupling method from probability theory to the game semantics of the probabilistic modal μ-calculus.