Abstract
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 ≡ ε s indexed by rationals, expressing that “t is approximately equal to s up to an error ε”. 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).
| Language | English |
|---|---|
| Article number | 15 |
| Number of pages | 29 |
| Journal | Logical Methods in Computer Science |
| Volume | 14 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 16 Nov 2018 |
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Keywords
- axiomatization
- behavioral distances
- Markov chains
Cite this
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A complete quantitative deduction system for the bisimilarity distance on Markov chains. / Bacci, Giorgio; Bacci, Giovanni; Larsen, Kim G.; Mardare, Radu.
In: Logical Methods in Computer Science, Vol. 14, No. 4, 15, 16.11.2018.Research output: Contribution to journal › Article
TY - JOUR
T1 - A complete quantitative deduction system for the bisimilarity distance on Markov chains
AU - Bacci, Giorgio
AU - Bacci, Giovanni
AU - Larsen, Kim G.
AU - Mardare, Radu
PY - 2018/11/16
Y1 - 2018/11/16
N2 - 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 ≡ ε s indexed by rationals, expressing that “t is approximately equal to s up to an error ε”. 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).
AB - 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 ≡ ε s indexed by rationals, expressing that “t is approximately equal to s up to an error ε”. 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).
KW - axiomatization
KW - behavioral distances
KW - Markov chains
UR - http://www.scopus.com/inward/record.url?scp=85060257142&partnerID=8YFLogxK
U2 - 10.23638/LMCS-14(4:15)2018
DO - 10.23638/LMCS-14(4:15)2018
M3 - Article
VL - 14
JO - Logical Methods in Computer Science
T2 - Logical Methods in Computer Science
JF - Logical Methods in Computer Science
SN - 1860-5974
IS - 4
M1 - 15
ER -