Interval Temporal Logic for Visibly Pushdown Systems

Authors Laura Bozzelli, Angelo Montanari, Adriano Peron

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Laura Bozzelli
  • University of Napoli "Federico II", Napoli, Italy
Angelo Montanari
  • University of Udine, Udine, Italy
Adriano Peron
  • University of Napoli "Federico II", Napoli, Italy

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Laura Bozzelli, Angelo Montanari, and Adriano Peron. Interval Temporal Logic for Visibly Pushdown Systems. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 33:1-33:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


In this paper, 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. Both homogeneity and visibility are assumed. 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 [R. Alur et al., 2004] and NWTL [R. Alur et al., 2007]. 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Pushdown systems
  • Interval temporal logic
  • Model checking


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