Equational Axioms for Probabilistic Bisimilarity
نویسندگان
چکیده
This paper gives an equational axiomatization of probabilistic bisimulation equivalence for a class of finite-state agents previously studied by Stark and Smolka ((2000) Proof, Language, and Interaction: Essays in Honour of Robin Milner, pp. 571–595). The axiomatization is obtained by extending the general axioms of iteration theories (or iteration algebras), which characterize the equational properties of the fixed point operator on (ω-)continuous or monotonic functions, with three axiom schemas that express laws that are specific to probabilistic bisimilarity. Hence probabilistic bisimilarity (over finite-state agents) has an equational axiomatization relative to iteration algebras.
منابع مشابه
Complete Axiomatization for the Bisimilarity Distance on Markov Chains
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’16) that uses equality relations t ≡ε s indexed by rationals, expressing that “t is approximately e...
متن کاملA Calculus of Dataaow Networks
Dataaow networks are a paradigm for concurrent computation in which a collection of concurrently and asynchronously executing processes communicate by sending data values over FIFO communication channels. In this paper, we deene a CCS-style calculus of dataaow networks with a standard structural operational semantics. A version of weak bisimulation equivalence, called \buuer bisimilarity," is d...
متن کاملA Complete Quantitative Deduction System for the Bisimilarity Distance on Markov Chains
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...
متن کاملAxiomatizing Bisimulation Equivalences and Metrics from Probabilistic SOS Rules
Probabilistic transition system specifications (PTSS) provide structural operational semantics for reactive probabilistic labeled transition systems. Bisimulation equivalences and bisimulation metrics are fundamental notions to describe behavioral relations and distances of states, respectively. We provide a method to generate from a PTSS a sound and ground-complete equational axiomatization fo...
متن کاملHennessy-Milner Completeness in Transition Systems with Synchronous Concurrent Composition
We consider the problem of obtaining Hennessy-Milner soundness and completeness-the coincidence of logical equivalence and bisimilarity-in the setting of transition systems with synchronous concurrent composition. Starting from a richly expressive modal logic, motivated by resource semantics and distributed systems modelling, including both additive and multiplicative propositional connectives ...
متن کامل