Tomorrow and All our Yesterdays: MTL Satisfiability over the Integers

  • Carlo A. Furia
  • Paola Spoletini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5160)

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Carlo A. Furia
    • 1
  • Paola Spoletini
    • 2
  1. 1.DEIPolitecnico di MilanoMilanoItaly
  2. 2.DSCPIUniversità degli Studi dell’InsubriaComoItaly

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