Efficient detection of vacuity in ACTL formulas

  • Ilan Beer
  • Shoham Ben-David
  • Cindy Eisner
  • Yoav Rodeh
Conference paper

DOI: 10.1007/3-540-63166-6_28

Part of the Lecture Notes in Computer Science book series (LNCS, volume 1254)
Cite this paper as:
Beer I., Ben-David S., Eisner C., Rodeh Y. (1997) Efficient detection of vacuity in ACTL formulas. In: Grumberg O. (eds) Computer Aided Verification. CAV 1997. Lecture Notes in Computer Science, vol 1254. Springer, Berlin, Heidelberg

Abstract

Prepositional logic formulas containing implications can suffer from antecedent failure, in which the formula is true trivially because the pre-condition of the implication is not satisfiable. In other words, the post-condition of the implication does not affect the truth value of the formula. We call this a vacuous pass, and extend the definition of vacuity to cover other kinds of trivial passes in temporal logic. We define w-ACTL, a subset of CTL and show by construction that for every w-ACTL formula ϕ there is a formula w(ϕ), such that: both ϕ and w(ϕ) are true in some model M iff ϕ passes vacuously. A useful side-effect of w(ϕ) is that if false, any counter-example is also a non-trivial witness of the original formula ϕ.

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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Ilan Beer
    • 1
  • Shoham Ben-David
    • 1
  • Cindy Eisner
    • 1
  • Yoav Rodeh
    • 1
  1. 1.Haifa Research LaboratoryIBM Science and TechnologyMatam, HaifaIsrael

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