Certificates for Probabilistic Pushdown Automata via Optimistic Value Iteration

Abstract Probabilistic pushdown automata (pPDA) are a standard model for discrete probabilistic programs with procedures and recursion. In pPDA, many quantitative properties characterized as least fixpoints of polynomial equation systems. this paper, we study the problem certifying that these quantities lie within certain bounds. To end, first characterize systems admit easy-to-check certificates validating bounds on their fixpoint. Second, present sound complete Optimistic Value Iteration algorithm computing such certificates. Third, show how can be transferred to various pPDA properties. Experiments demonstrate our computes succinct several intricate example well stochastic context-free grammars $$> 10^4$$ > 10 4 production rules.