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An In-Depth Investigation of Interval Temporal Logic Model Checking with Regular Expressions

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Software Engineering and Formal Methods (SEFM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10469))

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Abstract

In the last years, the model checking (MC) problem for interval temporal logic (ITL) has received an increasing attention as a viable alternative to the traditional (point-based) temporal logic MC, which can be recovered as a special case. Most results have been obtained by imposing suitable restrictions on interval labeling. In this paper, we overcome such limitations by using regular expressions to define the behavior of proposition letters over intervals in terms of the component states. We first prove that MC for Halpern and Shoham’s ITL (HS), extended with regular expressions, is decidable. Then, we show that formulas of a large class of HS fragments, namely, all fragments featuring (a subset of) HS modalities for Allen’s relations meets, met-by, starts, and started-by, can be model checked in polynomial working space (MC for all these fragments turns out to be PSPACE-complete).

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Notes

  1. 1.

    All the results we prove in the paper hold for the strict semantics as well.

  2. 2.

    As shown in [4], this is not the case in general: the computation-tree-based semantics of [10,11,12] is subsumed by the state-based one of [14] and follow-up papers.

  3. 3.

    The factor 2 in front of \(|\psi '|\) is needed as the small-model requires a formula in NNF.

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Correspondence to Angelo Montanari .

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Bozzelli, L., Molinari, A., Montanari, A., Peron, A. (2017). An In-Depth Investigation of Interval Temporal Logic Model Checking with Regular Expressions. In: Cimatti, A., Sirjani, M. (eds) Software Engineering and Formal Methods. SEFM 2017. Lecture Notes in Computer Science(), vol 10469. Springer, Cham. https://doi.org/10.1007/978-3-319-66197-1_7

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  • DOI: https://doi.org/10.1007/978-3-319-66197-1_7

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