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An Abstract Interpretation Perspective on Linear vs. Branching Time

  • Francesco Ranzato
  • Francesco Tapparo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3780)

Abstract

It is known that the branching time language ACTL and the linear time language ∀ LTL of universally quantified formulae of LTL have incomparable expressive powers, i.e., Sem(ACTL) and Sem(∀LTL) are incomparable sets. Within a standard abstract interpretation framework, ACTL can be viewed as an abstract interpretation LTL ∀  of LTL where the universal path quantifier ∀ abstracts each linear temporal operator of LTL to a corresponding branching state temporal operator of ACTL. In abstract interpretation terms, it turns out that the universal path quantifier abstraction of LTL is incomplete. In this paper we reason on a generic abstraction α over a domain A of a generic linear time language L. This approach induces both a language αL of α-abstracted formulae of L and an abstract language L α whose operators are the best correct abstractions in A of the linear operators of L. When the abstraction α is complete for the operators in L it turns out that α L and L α have the same expressive power, so that trace-based model checking of α L can be reduced with no lack of precision to A-based model checking of L α . This abstract interpretation-based approach allows to compare temporal languages at different levels of abstraction and to view the standard linear vs. branching time comparison as a particular instance.

Keywords

Model Check Complete Lattice Expressive Power Abstract Interpretation Atomic Proposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Francesco Ranzato
    • 1
  • Francesco Tapparo
    • 1
  1. 1.Dipartimento di Matematica Pura ed ApplicataUniversità di PadovaItaly

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