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A Decidable Temporal Logic of Repeating Values

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Logical Foundations of Computer Science (LFCS 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4514))

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Abstract

Various logical formalisms with the freeze quantifier have been recently considered to model computer systems even though this is a powerful mechanism that often leads to undecidability. In this paper, we study a linear-time temporal logic with past-time operators such that the freeze operator is only used to express that some value from an infinite set is repeated in the future or in the past. Such a restriction has been inspired by a recent work on spatio-temporal logics. We show decidability of finitary and infinitary satisfiability by reduction into the verification of temporal properties in Petri nets. This is a surprising result since the logic is closed under negation, contains future-time and past-time temporal operators and can express the nonce property and its negation. These ingredients are known to lead to undecidability with a more liberal use of the freeze quantifier.

Work supported by the Indo-French project “Timed-DISCOVERI” (P2R/RNP scheme).

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Authors and Affiliations

  1. LSV, ENS Cachan, CNRS, Inria,  

    Stéphane Demri & Régis Gascon

  2. Dept. of Computer Science & Automation, Indian Institute of Science, Bangalore, India

    Deepak D’Souza

Authors
  1. Stéphane Demri
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  2. Deepak D’Souza
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  3. Régis Gascon
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Sergei N. Artemov Anil Nerode

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Demri, S., D’Souza, D., Gascon, R. (2007). A Decidable Temporal Logic of Repeating Values. In: Artemov, S.N., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2007. Lecture Notes in Computer Science, vol 4514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72734-7_13

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  • DOI: https://doi.org/10.1007/978-3-540-72734-7_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72732-3

  • Online ISBN: 978-3-540-72734-7

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