Complete axiomatization for the total variation distance of Markov chains

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

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3 Citations (Scopus)
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We propose a complete axiomatization for the total variation distance of finite labelled Markov chains. Our axiomatization is given in the form of a quantitative deduction system, a framework recently proposed by Mardare, Panangaden, and Plotkin (LICS 2016) to extend classical equational deduction systems by means of inferences of equality relations t≡εs indexed by rationals, expressing that “t is approximately equal to s up to an error ε”. Notably, the quantitative equational system is obtained by extending our previous axiomatization (CONCUR 2016) for the probabilistic bisimilarity distance with a distributivity axiom for the prefix operator over the probabilistic choice inspired by Rabinovich's (MFPS 1983). Finally, we propose a metric extension to the Kleene-style representation theorem for finite labelled Markov chains w.r.t. trace equivalence due to Silva and Sokolova (MFPS 2011).

Original languageEnglish
Pages (from-to)27-39
Number of pages13
JournalElectronic Notes in Theoretical Computer Science
Publication statusPublished - 16 Apr 2018


  • axiomatization
  • behavioral distances
  • Markov chains
  • quantitative deductive systems


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