Model Checking Probabilistic Pushdown Automata

TL;DR

This paper establishes the decidability of various model checking problems for probabilistic pushdown automata (pPDA), including properties expressed in probabilistic logics like PCTL and omega-regular properties, and introduces an error-tolerant algorithm for certain cases.

Contribution

It proves the decidability of qualitative and quantitative model checking for pPDA across multiple probabilistic logics and develops an error-tolerant algorithm for stateless pPDA.

Findings

Decidability of qualitative and quantitative model checking for pPDA.

Decidability of model checking for PCTL and omega-regular properties on pPDA.

Development of an error-tolerant model checking algorithm for stateless pPDA.

Abstract

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.