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Acta Informatica

, Volume 53, Issue 6–8, pp 587–619 | Cite as

Checking interval properties of computations

  • Alberto Molinari
  • Angelo MontanariEmail author
  • Aniello Murano
  • Giuseppe Perelli
  • Adriano Peron
Original Article

Abstract

Model checking is a powerful method widely explored in formal verification. Given a model of a system, e.g., a Kripke structure, and a formula specifying its expected behaviour, one can verify whether the system meets the behaviour by checking the formula against the model. Classically, system behaviour is expressed by a formula of a temporal logic, such as LTL and the like. These logics are “point-wise” interpreted, as they describe how the system evolves state-by-state. However, there are relevant properties, such as those constraining the temporal relations between pairs of temporally extended events or involving temporal aggregations, which are inherently “interval-based”, and thus asking for an interval temporal logic. In this paper, we give a formalization of the model checking problem in an interval logic setting. First, we provide an interpretation of formulas of Halpern and Shoham’s interval temporal logic HS over finite Kripke structures, which allows one to check interval properties of computations. Then, we prove that the model checking problem for HS against finite Kripke structures is decidable by a suitable small model theorem, and we provide a lower bound to its computational complexity.

Notes

Acknowledgments

We would like to thank the anonymous reviewers whose comments and suggestions helped us to improve the paper. Angelo Montanari, Aniello Murano, and Adriano Peron acknowledge the support from the GNCS project: “Algorithmica for model checking and synthesis of safety-critical systems”. Aniello Murano and Adriano Peron also acknowledge the support from the FP7 EU Project 600958-SHERPA.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Alberto Molinari
    • 1
  • Angelo Montanari
    • 1
    Email author
  • Aniello Murano
    • 2
  • Giuseppe Perelli
    • 3
  • Adriano Peron
    • 2
  1. 1.Department of Mathematics and Computer ScienceUniversity of UdineUdineItaly
  2. 2.Department of Electronic Engineering and Information TechnologyUniversity of NaplesNaplesItaly
  3. 3.Department of Computer ScienceOxford UniversityOxfordUK

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