Efficient detection of vacuity in ACTL formulas

  • Ilan Beer
  • Shoham Ben-David
  • Cindy Eisner
  • Yoav Rodeh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1254)


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.


Model Check Temporal Logic Formal Verification Atomic Proposition Computation Path 
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Copyright information

© Springer-Verlag Berlin Heidelberg 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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