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Finite-Trace Linear Temporal Logic: Coinductive Completeness

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Book cover Runtime Verification (RV 2016)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10012))

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Abstract

Linear temporal logic (LTL) is suitable not only for infinite-trace systems, but also for finite-trace systems. Indeed, LTL is frequently used as a trace specification formalism in runtime verification. The completeness of LTL with only infinite or with both infinite and finite traces has been extensively studied, but similar direct results for LTL with only finite traces are missing. This paper proposes a sound and complete proof system for finite-trace LTL. The axioms and proof rules are natural and expected, except for one rule of coinductive nature, reminiscent of the Gödel-Löb axiom. A direct decision procedure for finite-trace LTL satisfiability, a PSPACE-complete problem, is also obtained as a corollary.

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Notes

  1. 1.

    See [2] for multi-valued variants of LTL.

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Authors and Affiliations

  1. University of Illinois, Champaign, USA

    Grigore Roşu

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  1. Grigore Roşu
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Correspondence to Grigore Roşu .

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Editors and Affiliations

  1. Université Grenoble Alpes, Inria, Grenoble, France

    Yliès Falcone

  2. IMDEA Software Institute, Madrid, Spain

    César Sánchez

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Roşu, G. (2016). Finite-Trace Linear Temporal Logic: Coinductive Completeness. In: Falcone, Y., Sánchez, C. (eds) Runtime Verification. RV 2016. Lecture Notes in Computer Science(), vol 10012. Springer, Cham. https://doi.org/10.1007/978-3-319-46982-9_21

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  • DOI: https://doi.org/10.1007/978-3-319-46982-9_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46981-2

  • Online ISBN: 978-3-319-46982-9

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