On randomization in sequential and distributed algorithms
ACM Computing Surveys (CSUR)
The complexity of probabilistic verification
Journal of the ACM (JACM)
Handbook of formal languages, vol. 3
Model checking
Distributed Algorithms
LPAR '02 Proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Computation: finite and infinite machines
Computation: finite and infinite machines
Checking LTL Properties of Recursive Markov Chains
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Principles of Model Checking (Representation and Mind Series)
Principles of Model Checking (Representation and Mind Series)
Automatic verification of probabilistic concurrent finite state programs
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Verification of probabilistic systems with faulty communication
Information and Computation
On the decidability of temporal properties of probabilistic pushdown automata
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects 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
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Model checking is a fully automatic verification technique traditionally used to verify finite-state systems against regular specifications. Although regular specifications have been proven to be feasible in practice, many desirable specifications are non-regular. For instance, requirements which involve counting cannot be formalized by regular specifications but using pushdown specifications, i.e., context-free properties represented by pushdown automata. Research on model-checking techniques for pushdown specifications is, however, rare and limited to the verification of non-probabilistic systems. In this paper, we address the probabilistic model-checking problem for systems modeled by discrete-time Markov chains and specifications that are provided by deterministic pushdown automata over infinite words. We first consider finite-state Markov chains and show that the quantitative and qualitative model-checking problem is solvable via a product construction and techniques that are known for the verification of probabilistic pushdown automata. Then, we consider recursive systems modeled by probabilistic pushdown automata with an infinite-state Markov chain semantics. We first show that imposing appropriate compatibility (visibility) restrictions on the synchronizations between the pushdown automaton for the system and the specification, decidability of the probabilistic model-checking problem can be established. Finally we prove that slightly departing from this compatibility assumption leads to the undecidability of the probabilistic model-checking problem, even for qualitative properties specified by deterministic context-free specifications.