Reference Work Entry

Encyclopedia of Parallel Computing

pp 136-139

# Bisimulation

• Robert J. van GlabbeekAffiliated withNICTAThe University of New South WalesStanford University

## 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 aA – (the transitions),such that for all sS the class ...

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