TY - JOUR
TI - Bisimulation for Labelled Markov Processes
AU - Desharnais, Josée
AU - Edalat, Abbas
AU - Panangaden, Prakash
T2 - Information and Computation
AB - 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. We assume that the state space is a certain type of common metric space called an analytic space. We show that our definition of probabilistic bisimulation generalizes the Larsen–Skou definition given for discrete systems. The formalism and mathematics is substantially different from the usual treatment of probabilistic process algebra. The main technical contribution of the paper is a logical characterization of probabilistic bisimulation. This study revealed some unexpected results, even for discrete probabilistic systems. •Bisimulation can be characterized by a very weak modal logic. The most striking feature is that one has no negation or any kind of negative proposition.•We do not need any finite branching assumption, yet there is no need of infinitary conjunction. We also show how to construct the maximal autobisimulation on a system. In the finite state case, this is just a state minimization construction. The proofs that we give are of an entirely different character than the typical proofs of these results. They use quite subtle facts about analytic spaces and appear, at first sight, to be entirely nonconstructive. Yet one can give an algorithm for deciding bisimilarity of finite state systems which constructs a formula that witnesses the failure of bisimulation.
DA - 2002/12/15/
PY - 2002
DO - 10/fmp9vd
DP - ScienceDirect
VL - 179
IS - 2
SP - 163
EP - 193
J2 - Information and Computation
LA - en
SN - 0890-5401
UR - http://www.sciencedirect.com/science/article/pii/S0890540101929621
Y2 - 2019/11/26/21:27:24
KW - Coalgebras
KW - Denotational semantics
KW - Probabilistic transition systems
KW - Symbolic logic
KW - Transition systems
ER -