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Theorem Proving for Metric Temporal Logic over the Naturals

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Automated Deduction – CADE 26 (CADE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10395))

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Abstract

We study translations from Metric Temporal Logic (MTL) over the natural numbers to Linear Temporal Logic (LTL). In particular, we present two approaches for translating from MTL to LTL which preserve the ExpSpace complexity of the satisfiability problem for MTL. In each of these approaches we consider the case where the mapping between states and time points is given by (1) a strict monotonic function and by (2) a non-strict monotonic function (which allows multiple states to be mapped to the same time point). Our translations allow us to utilise LTL solvers to solve satisfiability and we empirically compare the translations, showing in which cases one performs better than the other.

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Notes

  1. 1.

    We write \(\mathsf{min}(l+k,2\cdot C)\) for the minimum between \(l+k\) and \(2\cdot C\). If the minimum is \(2\cdot C\) then \( s^{j+1}_{2\cdot C} \) means that the sum of the last \(j+1\) variables is greater or equal to \(2\cdot C\).

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Authors and Affiliations

  1. Department of Computer Science, University of Liverpool, Liverpool, UK

    Ullrich Hustadt & Clare Dixon

  2. Center for Advancing Electronics Dresden (cfaed), TU Dresden, Dresden, Germany

    Ana Ozaki

Authors
  1. Ullrich Hustadt
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  2. Ana Ozaki
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  3. Clare Dixon
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Corresponding authors

Correspondence to Ullrich Hustadt or Ana Ozaki .

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Editors and Affiliations

  1. Microsoft Research, Redmond, Washington, USA

    Leonardo de Moura

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Hustadt, U., Ozaki, A., Dixon, C. (2017). Theorem Proving for Metric Temporal Logic over the Naturals . In: de Moura, L. (eds) Automated Deduction – CADE 26. CADE 2017. Lecture Notes in Computer Science(), vol 10395. Springer, Cham. https://doi.org/10.1007/978-3-319-63046-5_20

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  • DOI: https://doi.org/10.1007/978-3-319-63046-5_20

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  • Online ISBN: 978-3-319-63046-5

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