Interval Temporal Logic for Visibly Pushdown Systems

Abstract

In this article, we introduce and investigate an extension of Halpern and Shoham’s interval temporal logic HS for the specification and verification of branching-time context-free requirements of pushdown systems under a state-based semantics over Kripke structures enforcing visibility of the pushdown operations. The proposed logic, called nested BHS , supports branching-time both in the past and in the future and is able to express non-regular properties of linear and branching behaviours of procedural contexts in a natural way. It strictly subsumes well-known linear time context-free extensions of LTL such as CaRet  [ 4 ] and NWTL  [ 2 ]. The main result is the decidability of the visibly pushdown model-checking problem against nested BHS . The proof exploits a non-trivial automata-theoretic construction.