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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 =_e s indexed by rationals, expressing that “t is approximately equal to s up to an error e”. 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 language | English |
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Journal | Electronic Notes in Theoretical Computer Science |
Volume | 336 |
Pages (from-to) | 27-39 |
Number of pages | 13 |
ISSN | 1571-0661 |
DOIs | |
Publication status | Published - 16 Apr 2018 |
Event | Mathematical Foundations of Programming Semantics XXXIII - Faculty of Mathematics and Physics in Ljubljana, Ljubljana, Slovenia Duration: 12 Jul 2017 → 16 Jul 2017 http://coalg.org/mfps-calco2017/ |
Conference
Conference | Mathematical Foundations of Programming Semantics XXXIII |
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Location | Faculty of Mathematics and Physics in Ljubljana |
Country/Territory | Slovenia |
City | Ljubljana |
Period | 12/07/2017 → 16/07/2017 |
Internet address |
Keywords
- Axiomatization
- Behavioral Distances
- Markov Chains
- Quantitative Deductive Systems
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- 1 Finished
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Approximate Reasoning for Stochastic Markovian Systems
Mardare, R. & Larsen, K. G.
01/11/2015 → 31/10/2019
Project: Research