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Beyond vacuity: towards the strongest passing formula

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Abstract

Given an LTL formula φ in negation normal form, it can be strengthened by replacing some of its literals with false. Given such a formula and a model M that satisfies it, vacuity and mutual vacuity attempt to find one or a maximal set of literals, respectively, with which φ can be strengthened while still being satisfied by M. We study the problem of finding the strongest LTL formula that satisfies M and is in the Boolean closure of strengthened versions of φ as defined above. This formula is stronger or equally strong to any formula that can be obtained by vacuity and mutual vacuity. We present our algorithms in the framework of lattice automata.

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Notes

  1. The formula vac(M,φ) was already introduced in [13] in the context of CTL formulas.

  2. That is, C φ is a surjective function from the paths of M to the disjuncts of Φ(M,φ).

  3. This example demonstrates the difference between formulas in which each subformula occurs only once and formulas in which subformulas can occur more than once but we treat each occurrence separately. We thank Orna Kupferman for bringing this difference to our attention.

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Authors and Affiliations

  1. Department of Informatics, King’s College London, London, UK

    Hana Chockler

  2. Software Engineering Institute, Pittsburgh, PA, USA

    Arie Gurfinkel

  3. Information Systems Engineering, IE, Technion, Haifa, Israel

    Ofer Strichman

Authors
  1. Hana Chockler
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  2. Arie Gurfinkel
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  3. Ofer Strichman
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Correspondence to Ofer Strichman.

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Chockler, H., Gurfinkel, A. & Strichman, O. Beyond vacuity: towards the strongest passing formula. Form Methods Syst Des 43, 552–571 (2013). https://doi.org/10.1007/s10703-013-0192-6

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