Tomorrow and All our Yesterdays: MTL Satisfiability over the Integers

Authors:
Carlo A. Furia;Paola Spoletini
Affiliations:
DEI, Politecnico di Milano, Milano, Italy;DSCPI, Università degli Studi dell'Insubria, Como, Italy
Venue:
Proceedings of the 5th international colloquium on Theoretical Aspects of Computing
Year:
2008

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Abstract

We investigate the satisfiability problem for metric temporal logic (MTL) with both past and future operators over linear discrete bi-infinite time models isomorphic to the integer numbers, where time is unbounded both in the future and in the past. We provide a technique to reduce satisfiability over the integers to satisfiability over the well-known mono-infinite time model of natural numbers, and we show how to implement the technique through an automata-theoretic approach. We also prove that MTL satisfiability over the integers is EXPSPACE-complete, hence the given algorithm is optimal in the worst case.