Deciding probabilistic bisimilarity over infinite-state probabilistic systems

We prove that probabilistic bisimilarity is decidable over probabilistic extensions of BPA and BPP processes. For normed subclasses of probabilistic BPA and BPP processes we obtain polynomial-time algorithms. Further, we show that probabilistic bisimilarity between probabilistic pushdown automata and finite-state systems is decidable in exponential time. If the number of control states in PDA is bounded by a fixed constant, then the algorithm needs only polynomial time. The work has been supported by the research centre Institute for Theoretical Computer Science (ITI), project No. 1M0545.