Complete axiomatization for the total variation distance of Markov chains

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)
18 Downloads (Pure)

Abstract

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
Volume336
DOIs
Publication statusPublished - 16 Apr 2018
Event33rd Conference on the Mathematical Foundations of Programming Semantics - Ljubljana, Slovenia
Duration: 12 Jun 201715 Jun 2017

Funding

This work has been supported by the EU 7th Framework Programme (FP7/2007-13) under Grants Agreement nr.318490 (SENSATION), nr.601148 (CASSTING), the Sino-Danish Basic Research Center IDEA4CPS funded by Danish National Research Foundation and National Science Foundation China, the ASAP Project (4181-00360) funded by the Danish Council for Independent Research, the ERC Advanced Grant LASSO, and the Innovation Fund Denmark center DiCyPS.

Keywords

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

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