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Complete Axiomatization for the Bisimilarity Distance on Markov Chains

Authors Giorgio Bacci, Giovanni Bacci, Kim G. Larsen, Radu Mardare

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Giorgio Bacci
Giovanni Bacci
Kim G. Larsen
Radu Mardare

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Giorgio Bacci, Giovanni Bacci, Kim G. Larsen, and Radu Mardare. Complete Axiomatization for the Bisimilarity Distance on Markov Chains. In 27th International Conference on Concurrency Theory (CONCUR 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 59, pp. 21:1-21:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.CONCUR.2016.21

Abstract

In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS'16) that uses equality relations t =_e s indexed by rationals, expressing that "t is approximately equal to s up to an error e".
Notably, our quantitative deductive system extends in a natural way the equational system for probabilistic bisimilarity given by Stark and Smolka by introducing an axiom for dealing with the Kantorovich distance between probability distributions.

Subject Classification

Keywords
  • Markov chains
  • Behavioral distances
  • Axiomatization

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