Model Checking Temporal Properties of Recursive Probabilistic Programs

Probabilistic pushdown automata (pPDA) are a standard operational model for programming languages involving discrete random choices, procedures, and returns. Temporal properties are useful for gaining insight into 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 study the model checking problem of pPDA against $\omega$-visibly pushdown languages that can be described by specification logics such as CaRet and are strictly more expressive than $\omega$-regular properties. 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.