## Bacci, Giorgio and Bacci, Giovanni and Larsen, Kim G. and Mardare, Radu - A Complete Quantitative Deduction System for the Bisimilarity Distance on Markov Chains

lmcs:3130 - Logical Methods in Computer Science, November 16, 2018, Volume 14, Issue 4
A Complete Quantitative Deduction System for the Bisimilarity Distance on Markov Chains

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

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 2016) that uses equality relations $t \equiv_\varepsilon s$ indexed by rationals, expressing that `$t$ is approximately equal to $s$ up to an error $\varepsilon$'. Notably, our quantitative deduction 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. The axiomatization is then used to propose a metric extension of a Kleene's style representation theorem for finite labelled Markov chains, that was proposed (in a more general coalgebraic fashion) by Silva et al. (Inf. Comput. 2011).

Source : oai:arXiv.org:1702.02528
DOI : 10.23638/LMCS-14(4:15)2018
Volume: Volume 14, Issue 4
Published on: November 16, 2018
Submitted on: February 9, 2017
Keywords: Computer Science - Logic in Computer Science