Bisimulation

Synonyms

Bisimulation equivalence; Bisimilarity

Definition

Bisimulation equivalence is a semantic equivalence relation on labeled transition systems, which are used to represent distributed systems. It identifies systems with the same branching structure.

Discussion

Labeled Transition Systems

A labeled transition system consists of a collection of states and a collection of transitions between them. The transitions are labeled by actions from a given set A that happen when the transition is taken, and the states may be labeled by predicates from a given set P that hold in that state.

Definition 1

Let A and P be sets (of actions and predicates, respectively).

A labeled transition system (LTS) over A and P is a triple $(S,\rightarrow,\models )$ with:

• S a class (of states).

• → a collection of binary relations ${\mathop \rightarrow \limits ^{a}}\; \subseteq S \times S$ – one for every a ∈ A – (the transitions),such that for all s ∈ S the class \(\{t \in S\mid s{\mathop \rightarrow...