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The Unary Fragments of Metric Interval Temporal Logic: Bounded versus Lower Bound Constraints

  • Paritosh K. Pandya
  • Simoni S. Shah
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7561)

Abstract

We study two unary fragments of the well-known metric interval temporal logic \(\mathit{MITL[\textsf{U}_I,\textsf{S}_I]}\) that was originally proposed by Alur and Henzinger, and we pin down their expressiveness as well as satisfaction complexities. We show that \(\mbox{$\mathit{MITL[\textsf{F}_\infty,\textsf{P}_\infty]}$}\) which has unary modalities with only lower-bound constraints is (surprisingly) expressively complete for Partially Ordered 2-Way Deterministic Timed Automata (po2DTA) and the reduction from logic to automaton gives us its NP-complete satisfiability. We also show that the fragment \(\mbox{$\mathit{MITL[\textsf{F}_b,\textsf{P}_b]}$}\) having unary modalities with only bounded intervals has NEXPTIME-complete satisfiability. But strangely, \(\mathit{MITL[\textsf{F}_b,\textsf{P}_b]}\) is strictly less expressive than \(\mathit{MITL[\textsf{F}_\infty,\textsf{P}_\infty]}\). We provide a comprehensive picture of the decidability and expressiveness of various unary fragments of MITL.

Keywords

Normal Form Temporal Logic Time Stamp Regular Language Unary Modality 
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 2012

Authors and Affiliations

  • Paritosh K. Pandya
    • 1
  • Simoni S. Shah
    • 1
  1. 1.Tata Institute of Fundamental ResearchMumbaiIndia

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