Model Checking Temporal Properties of Recursive Probabilistic Programs

TL;DR

This paper investigates the decidability and complexity of model checking probabilistic pushdown automata against structured temporal properties expressed in logics like CaRet, enabling verification of recursive probabilistic programs.

Contribution

It extends model checking to probabilistic pushdown automata with -visibly pushdown languages and CaRet logic, capturing structured procedural properties.

Findings

Decidability results for pPDA against -visibly pushdown languages.

Complexity analysis of the model checking problem.

Application to verifying correctness of recursive probabilistic programs.

Abstract

Probabilistic pushdown automata (pPDA) are a standard operational model for programming languages involving discrete random choices and recursive procedures. Temporal properties are useful for specifying the chronological order of events during program execution. Existing approaches for model checking pPDA against temporal properties have focused mostly on $\omega$-regular and LTL properties. In this paper, we give decidability and complexity results for the model checking problem of pPDA against $\omega$-visibly pushdown languages that can be described by specification logics such as CaRet. These logical formulae allow specifying properties that explicitly take the structured computations arising from procedural programs into account. For example, CaRet is able to match procedure calls with their corresponding future returns, and thus allows to express fundamental program properties such as total and partial correctness.