Strong preservation of temporal fixpoint-based operators by abstract interpretation

  • Authors:
  • Francesco Ranzato;Francesco Tapparo

  • Affiliations:
  • Dipartimento di Matematica Pura ed Applicata, Università di Padova, Italy;Dipartimento di Matematica Pura ed Applicata, Università di Padova, Italy

  • Venue:
  • VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
  • Year:
  • 2006

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Abstract

Standard abstract model checking relies on abstract Kripke structures which approximate the concrete model by gluing together indistinguishable states. Strong preservation for a specification language $\mathcal{L}$ encodes the equivalence of concrete and abstract model checking of formulas in $\mathcal{L}$. Abstract interpretation allows to design abstract models which are more general than abstract Kripke structures. In this paper we show how abstract interpretation-based models can be exploited in order to specify a general strongly preserving abstract model checking framework. This is shown in particular for specification languages including standard temporal operators which admit a characterization as least/greatest fixpoints, as e.g. standard “Finally”, “Globally”, “Until” and “Release” modalities.