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Model checking probabilistic pushdown automata. (English) Zbl 1126.68053
Summary: We consider the model checking problem for probabilistic pushdown automata (pPDA) and properties expressible in various probabilistic logics. We start with properties that can be formulated as instances of a generalized random walk problem. We prove that both qualitative and quantitative model checking for this class of properties and pPDA is decidable. Then we show that model checking for the qualitative fragment of the logic PCTL and pPDA is also decidable. Moreover, we develop an error-tolerant model checking algorithm for PCTL and the subclass of stateless pPDA. Finally, we consider the class of omega-regular properties and show that both qualitative and quantitative model checking for pPDA is decidable.

MSC:
68Q60 Specification and verification (program logics, model checking, etc.)
03B44 Temporal logic
68Q45 Formal languages and automata
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