Temporal Logics of Repeating Values

Demri, Stephane and D'Souza, Deepak and Gascon, Regis (2012) Temporal Logics of Repeating Values. In: JOURNAL OF LOGIC AND COMPUTATION, 22 (5). pp. 1059-1096.

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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 article, 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 that suggests such a restricted use of the freeze operator. We show decidability of finitary and infinitary satisfiability by reduction into the verification of temporal properties in Petri nets by proposing a symbolic representation of models. This is a quite surprising result in view of the expressive power of the logic 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. The article also contains developments about the relationships between temporal logics with the freeze operator and counter automata as well as reductions into first-order logics over data words.

Item Type:	Journal Article
Publication:	JOURNAL OF LOGIC AND COMPUTATION
Publisher:	OXFORD UNIV PRESS
Additional Information:	Copyright for this article belongs to OXFORD UNIV PRESS, ENGLAND
Keywords:	Temporal logics;freeze quantifier;logical methods in program verification
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	07 Dec 2012 08:35
Last Modified:	07 Dec 2012 08:35
URI:	http://eprints.iisc.ac.in/id/eprint/45315

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