Axiomatizing Bisimulation Equivalences and Metrics from Probabilistic SOS Rules
نویسندگان
چکیده
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 for strong and convex bisimilarity. The construction is based on the method of Aceto, Bloom and Vaandrager developed for non-deterministic transition system specifications. The novelty in our approach is to employ many-sorted algebras to axiomatize separately non-deterministic choice, probabilistic choice and their interaction. Furthermore, we generalize this method to axiomatize the strong and convex metric bisimulation distance of PTSS.
منابع مشابه
SOS rule formats for convex and abstract probabilistic bisimulations
Probabilistic transition system specifications (PTSSs) in the ntμfθ/ntμxθ format provide structural operational semantics for Segala-type systems that exhibit both probabilistic and nondeterministic behavior and guarantee that bisimilarity is a congruence for all operator defined in such format. Starting from the ntμfθ/ntμxθ, we obtain restricted formats that guarantee that three coarser bisimu...
متن کاملAxiomatizing St Bisimulation for a Process Algebra with Recursion and Action Reenement (extended Abstract)
Due to the complex nature of bisimulation equivalences which express some form of history dependence, it turned out to be problematic to axiomatize them for non trivial classes of systems. Here we introduce the idea of \compositional level-wise renaming" which gives rise to the new possibility of axiomatizing the class of history dependent bisimulations with slight modiications to the machinery...
متن کاملGame Refinement Relations and Metrics
We consider two-player games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose probability distributions over moves, rather than single moves. Given a goal (e.g., “reach a target state”), the question of winning is thus a probabilistic one...
متن کاملar X iv : 0 80 6 . 49 56 v 1 [ cs . L O ] 3 0 Ju n 20 08 GAME REFINEMENT RELATIONS AND METRICS
We consider two-player games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose probability distributions over moves, rather than single moves. Given a goal (e.g., " reach a target state "), the question of winning is thus a probabilistic o...
متن کاملAxiomatizing GSOS with Predicates
In this paper, we introduce an extension of the GSOS rule format with predicates such as termination, convergence and divergence. For this format we generalize the technique proposed by Aceto, Bloom and Vaandrager for the automatic generation of ground-complete axiomatizations of bisimilarity over GSOS systems. Our procedure is implemented in a tool that receives SOS specifications as input and...
متن کامل