Distribution-Based Bisimulation for Labelled Markov Processes
نویسندگان
چکیده
In this paper we propose a (sub)distribution-based bisimulation for labelled Markov processes and compare it with earlier definitions of state and event bisimulation, which both only compare states. In contrast to those state-based bisimulations, our distribution bisimulation is weaker, but corresponds more closely to linear properties. We construct a logic and a metric to describe our distribution bisimulation and discuss linearity, continuity and compositional properties.
منابع مشابه
Bisimulation for Labelled Markov Processes
In this paper we introduce a new class of labelled transition systems Labelled Markov Processes and define bisimulation for them. Labelled Markov processes are probabilistic labelled transition systems where the state space is not necessarily discrete, it could be the reals, for example. We assume that it is a Polish space (the underlying topological space for a complete separable metric space)...
متن کاملApproximating labelled Markov processes
Labelled Markov processes are probabilistic versions of labelled transition systems. In general, the state space of a labelled Markov process may be a continuum. In this paper, we study approximation techniques for continuous-state labelled Markov processes. We show that the collection of labelled Markov processes carries a Polish-space structure with a countable basis given by finite-state Mar...
متن کاملApproximating Labelled Markov Processes Again!
Labelled Markov processes are continuous-state fully probabilistic labelled transition systems. They can be seen as co-algebras of a suitable monad on the category of measurable space. The theory as developed so far included a treatment of bisimulation, logical characterization of bisimulation, weak bisimulation, metrics, universal domains for LMPs and approximations. Much of the theory involve...
متن کاملExpressiveness of Probabilistic Modal Logics, Revisited
Labelled Markov processes are probabilistic versions of labelled transition systems. In general, the state space of a labelled Markov process may be a continuum. Logical characterizations of probabilistic bisimulation and simulation were given by Desharnais et al. These results hold for systems defined on analytic state spaces and assume that there are countably many labels in the case of bisim...
متن کاملExpressiveness of Probabilistic Modal Logics
Labelled Markov processes are probabilistic versions of labelled transition systems. In general, the state space of a labelled Markov process may be a continuum. Logical characterizations of probabilistic bisimulation and simulation were given by Desharnais et al. These results hold for systems defined on analytic state spaces and assume that there are countably many labels in the case of bisim...
متن کامل