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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 omega-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.
|Title of host publication||Foundations of Software Science and Computation Structures : 18th International Conference, FOSSACS 2015, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2015, London, UK, April 11-18, 2015, Proceedings|
|Number of pages||15|
|Publication status||Published - 2015|
|Event||18th International Conference on Foundations of Software Science and Computation Structures - Queen Mary University, London, United Kingdom|
Duration: 11 Apr 2015 → 18 Apr 2015
Conference number: 18
|Conference||18th International Conference on Foundations of Software Science and Computation Structures|
|Location||Queen Mary University|
|Period||11/04/2015 → 18/04/2015|
|Series||Lecture Notes in Computer Science|
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- 3 Finished
01/04/2013 → 31/03/2016