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Optimal Proofs for Linear Temporal Logic on Lasso Words

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Automated Technology for Verification and Analysis (ATVA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11138))

Abstract

Counterexamples produced by model checkers can be hard to grasp. Often it is not even evident why a trace violates a specification. We show how to provide easy-to-check evidence for the violation of a linear temporal logic (LTL) formula on a lasso word, based on a novel sound and complete proof system for LTL on lasso words. Valid proof trees in our proof system follow the syntactic structure of the formula and provide insight on why each Boolean or temporal operator is violated or satisfied. We introduce the notion of optimal proofs with respect to a user-specified preference order and identify sufficient conditions for efficiently computing optimal proofs. We design and evaluate an algorithm that performs this computation, demonstrating that it can produce optimal proofs for complex formulas in under a second.

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Acknowledgment

We thank Srđan Kristić, Felix Klaedtke, and Joshua Schneider for discussions on using proof trees as explanations. Srđan Kristić, Karel Kubíček, and anonymous reviewers provided useful comments on early drafts of this paper. This work is supported by the Swiss National Science Foundation grant Big Data Monitoring (167162).

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Authors and Affiliations

  1. Institute of Information Security, Department of Computer Science, ETH Zürich, Zurich, Switzerland

    David Basin, Bhargav Nagaraja Bhatt & Dmitriy Traytel

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  1. David Basin
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  2. Bhargav Nagaraja Bhatt
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  3. Dmitriy Traytel
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Corresponding authors

Correspondence to Bhargav Nagaraja Bhatt or Dmitriy Traytel .

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Editors and Affiliations

  1. Microsoft Research, Redmond, WA, USA

    Shuvendu K. Lahiri

  2. University of Southern California, Los Angeles, CA, USA

    Chao Wang

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Basin, D., Bhatt, B.N., Traytel, D. (2018). Optimal Proofs for Linear Temporal Logic on Lasso Words. In: Lahiri, S., Wang, C. (eds) Automated Technology for Verification and Analysis. ATVA 2018. Lecture Notes in Computer Science(), vol 11138. Springer, Cham. https://doi.org/10.1007/978-3-030-01090-4_3

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  • DOI: https://doi.org/10.1007/978-3-030-01090-4_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-01089-8

  • Online ISBN: 978-3-030-01090-4

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