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An automata-theoretic decision procedure for Future Interval Logic

  • Y. S. Ramakrishna
  • L. K. Dillon
  • L. E. Moser
  • P. M. Melliar-Smith
  • G. Kutty
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 652)

Abstract

Graphical Interval Logic (GIL) is a temporal logic in which all reasoning is done by means of diagrammatic formulæ. It is a discrete linear-time modal logic in which the basic temporal modality is the interval. Future Interval Logic (FIL) provides the logical foundation for GIL. In this paper we present an automata-theoretic decision procedure for FIL with complexity DTIME\((2^{O(n^k )} )\), where n is the size of the formula and k is the depth of interval nesting. For formulæ with bounded depth but length unbounded, the satisfiability problem for FIL is shown to be PSPACE-complete. We believe that this is the first result giving a direct decision procedure of elementary complexity for an interval logic. We also show that the logic is transparent to finite stuttering over the class of ω-sequences, a feature that is useful for composition and refinement.

Keywords

Temporal Logic Decision Procedure World Model Propositional Dynamic Logic Interval Logic 
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 1992

Authors and Affiliations

  • Y. S. Ramakrishna
    • 1
  • L. K. Dillon
    • 1
  • L. E. Moser
    • 1
  • P. M. Melliar-Smith
    • 1
  • G. Kutty
    • 1
  1. 1.Departments of Electrical and Computer Engineering and of Computer ScienceUniversity of CaliforniaSanta BarbaraUSA

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