On the Total Variation Distance of Semi-Markov Chains

  • Giorgio BacciEmail author
  • Giovanni Bacci
  • Kim Guldstrand Larsen
  • Radu Mardare
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9034)


Semi-Markov chains (SMCs) are continuous-time probabilistic transition systems where the residence time on states is governed by generic distributions on the positive real line.

This paper shows the tight relation between the total variation distance on SMCs and their model checking problem over linear real-time specifications. Specifically, we prove that the total variation between two SMCs coincides with the maximal difference w.r.t. the likelihood of satisfying arbitrary MTL formulas or ω-languages recognized by timed automata.

Computing this distance (i.e., solving its threshold problem) is NP-hard and its decidability is an open problem. Nevertheless, we propose an algorithm for approximating it with arbitrary precision.


Model Check Measurable Space Coupling Structure Arbitrary Precision Total Variation Distance 
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 2015

Authors and Affiliations

  • Giorgio Bacci
    • 1
    Email author
  • Giovanni Bacci
    • 1
  • Kim Guldstrand Larsen
    • 1
  • Radu Mardare
    • 1
  1. 1.Department of Computer ScienceAalborg UniversityAalborgDenmark

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