In theoretical computer science, probabilistic bisimulation is an extension of the concept of bisimulation for fully probabilistic transition systems first described by K.G.
[1] A discrete probabilistic transition system is a triple where
It is assumed that the actions are chosen nondeterministically by an adversary or by the environment.
The definition of a probabilistic bisimulation on a system S is an equivalence relation R on the state space St, such that for every pair s,t in St with sRt and for every action a in Act and for every equivalence class C of R
When applied to Markov chains, probabilistic bisimulation is the same concept as lumpability.