Giorgio Bacci ; Giovanni Bacci ; Kim G. Larsen ; Radu Mardare - 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 - https://doi.org/10.23638/LMCS-14(4:15)2018
A Complete Quantitative Deduction System for the Bisimilarity Distance on Markov ChainsArticle

Authors: Giorgio Bacci ORCID; Giovanni Bacci ORCID; Kim G. Larsen ; Radu Mardare

    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).


    Volume: Volume 14, Issue 4
    Published on: November 16, 2018
    Accepted on: November 14, 2018
    Submitted on: February 9, 2017
    Keywords: Computer Science - Logic in Computer Science
    Funding:
      Source : OpenAIRE Graph
    • Learning, Analysis, SynthesiS and Optimization of Cyber-Physical Systems; Funder: European Commission; Code: 669844
    • Self Energy-Supporting Autonomous Computation; Funder: European Commission; Code: 318490
    • Collective Adaptive System SynThesIs with Non-zero-sum Games; Funder: European Commission; Code: 601148

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