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Bisimulation : ウィキペディア英語版
Bisimulation
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.
== Formal definition ==
Given a labelled state transition system (S, Λ, →), a ''bisimulation'' relation is a binary relation R over S (i.e., RS × S) such that both R−1 and R are simulations.
Equivalently R is a bisimulation if for every pair of elements p, q in S with (p,q) in R, for all α in Λ:
for all p' in S,
::
p \overset p'

:implies that there is a q' in S such that
::
q \overset q'

:and (p',q') \in R;
and, symmetrically, for all q' in S
::
q \overset q'

:implies that there is a p' in S such that
::
p \overset p'

:and (p',q') \in R.
Given two states p and q in S, p is bisimilar to q, written p \, \sim \, q, if there is a bisimulation R such that (p, q) is in R.
The bisimilarity relation \, \sim \, is an equivalence relation. Furthermore, it is the largest bisimulation relation over a given transition system.
Note that it is not always the case that if p simulates q and q simulates p then they are bisimilar. For p and q to be bisimilar, the simulation between p and q must be the inverse of the simulation between q and p. Counter-example (in CCS, describing a coffee machine) : M=p.\overline.M+p.\overline.M+p.(\overline.M+\overline.M) and M'=p.(\overline.M'+\overline.M') simulate each other but are not bisimilar.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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