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Parametric Metric Interval Temporal Logic

  • Barbara Di Giampaolo
  • Salvatore La Torre
  • Margherita Napoli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6031)

Abstract

We study an extension of the logic MITL with parametric constants. In particular, we define a logic, denoted PMITL (parametric MITL), where the subscripts of the temporal operators are intervals with possibly a parametric endpoint. We consider typical decision problems, such as emptiness and universality of the set of parameter valuations under which a given parametric formula is satisfiable, or whether a given parametric timed automaton is a model of a given parametric formula. We show that when each parameter is used with a fixed polarity and only parameter valuations which evaluate parametric intervals to non-singular time intervals are taken into consideration, then the considered problems are decidable and Expspace-complete. We also investigate the computational complexity of these problems for natural fragments of PMITL, and show that in meaningful fragments of the logic they are Pspace-complete. Finally, we discuss other natural parameterizations of MITL, which indeed lead to undecidability.

Keywords

Model Check Temporal Logic Linear Temporal Logic Parametric Interval Parametric Expression 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Barbara Di Giampaolo
    • 1
  • Salvatore La Torre
    • 1
  • Margherita Napoli
    • 1
  1. 1.Università degli Studi di SalernoFiscianoItaly

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