Quantifying Similarities Between Timed Systems

  • Thomas A. Henzinger
  • Rupak Majumdar
  • Vinayak S. Prabhu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3829)

Abstract

We define quantitative similarity functions between timed transition systems that measure the degree of closeness of two systems as a real, in contrast to the traditional boolean yes/no approach to timed simulation and language inclusion. Two systems are close if for each timed trace of one system, there exists a corresponding timed trace in the other system with the same sequence of events and closely corresponding event timings. We show that timed CTL is robust with respect to our quantitative version of bisimilarity, in particular, if a system satisfies a formula, then every close system satisfies a close formula. We also define a discounted version of CTL over timed systems, which assigns to every CTL formula a real value that is obtained by discounting real time. We prove the robustness of discounted CTL by establishing that close states in the bisimilarity metric have close values for all discounted CTL formulas.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Thomas A. Henzinger
    • 1
  • Rupak Majumdar
    • 2
  • Vinayak S. Prabhu
    • 3
  1. 1.Department of Computer and Communication SciencesEPFL 
  2. 2.Department of Computer ScienceUC Los Angeles 
  3. 3.Department of Electrical Engineering and Computer SciencesUC Berkeley 

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