The complexity of probabilistic verification
Journal of the ACM (JACM)
General decidability theorems for infinite-state systems
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Quantitative Analysis and Model Checking
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
Model Checking Probabilistic Pushdown Automata
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Limiting Behavior of Markov Chains with Eager Attractors
QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
Automatic verification of probabilistic concurrent finite state programs
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Recursive markov chains, stochastic grammars, and monotone systems of nonlinear equations
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
ATVA'06 Proceedings of the 4th international conference on Automated Technology for Verification and Analysis
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We give en example-guided introduction to a framework that we have developed in recent years in order to extend the applicability of program verification to the context of systems modeled as infinite-state Markov chains. In particular, we describe the class of decisive Markov chains, and show how to perform qualitative and quantitative analysis of Markov chains that arise from probabilistic extensions of classical models such as Petri nets and communicating finite-state processes.