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Linear Distances between Markov Chains

Authors Przemyslaw Daca, Thomas A. Henzinger, Jan Kretinsky, Tatjana Petrov

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Przemyslaw Daca
Thomas A. Henzinger
Jan Kretinsky
Tatjana Petrov

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Przemyslaw Daca, Thomas A. Henzinger, Jan Kretinsky, and Tatjana Petrov. Linear Distances between Markov Chains. In 27th International Conference on Concurrency Theory (CONCUR 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 59, pp. 20:1-20:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.CONCUR.2016.20

Abstract

We introduce a general class of distances (metrics) between Markov chains, which are based on linear behaviour. This class encompasses distances given topologically (such as the total variation distance or trace distance) as well as by temporal logics or automata. We investigate which of the distances can be approximated by observing the systems, i.e. by black-box testing or simulation, and we provide both negative and positive results.
Keywords
  • probabilistic systems
  • verification
  • statistical model checking
  • temporal logic
  • behavioural equivalence

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