Bisimilarity

In theoretical computer science a bisimulation is a binary relation between state transition systems, associating systems that behave in the same way in the sense that one system simulates the other and vice versa.

Intuitively two systems are bisimilar if they match each other's moves. In this sense, each of the systems cannot be distinguished from the other by an observer.

Given a labelled state transition system (${\displaystyle S}$, Λ, →), a bisimulation relation is a binary relation ${\displaystyle R}$ over ${\displaystyle S}$ (i.e., ${\displaystyle R}$ ⊆ ${\displaystyle S}$ × ${\displaystyle S}$) such that both ${\displaystyle R}$ and its inverse ${\displaystyle R^{-1}}$ are simulations.

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