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Published in:
2015 | OriginalPaper | Chapter
On the Total Variation Distance of Semi-Markov Chains
Authors : Giorgio Bacci, Giovanni Bacci, Kim Guldstrand Larsen, Radu Mardare
Published in: Foundations of Software Science and Computation Structures
Publisher: Springer Berlin Heidelberg
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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.