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From liveness to promptness

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Abstract

Liveness temporal properties state that something “good” eventually happens, e.g., every request is eventually granted. In Linear Temporal Logic (LTL), there is no a priori bound on the “wait time” for an eventuality to be fulfilled. That is, F θ asserts that θ holds eventually, but there is no bound on the time when θ will hold. This is troubling, as designers tend to interpret an eventuality F θ as an abstraction of a bounded eventuality F ≤k θ, for an unknown k, and satisfaction of a liveness property is often not acceptable unless we can bound its wait time. We introduce here prompt-LTL, an extension of LTL with the prompt-eventually operator F p . A system S satisfies a prompt-LTL formula φ if there is some bound k on the wait time for all prompt-eventually subformulas of φ in all computations of S. We study various problems related to prompt-LTL, including realizability, model checking, and assume-guarantee model checking, and show that they can be solved by techniques that are quite close to the standard techniques for LTL.

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Authors and Affiliations

  1. Hebrew University, Jerusalem, Israel

    Orna Kupferman

  2. Imperial College, London, UK

    Nir Piterman

  3. Rice University, Houston, USA

    Moshe Y. Vardi

Authors
  1. Orna Kupferman
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  2. Nir Piterman
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  3. Moshe Y. Vardi
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Correspondence to Orna Kupferman.

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Kupferman, O., Piterman, N. & Vardi, M.Y. From liveness to promptness. Form Methods Syst Des 34, 83–103 (2009). https://doi.org/10.1007/s10703-009-0067-z

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  • DOI: https://doi.org/10.1007/s10703-009-0067-z

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