transitive closure

The transitive closure R* of a relation R is defined by

 x R y => x R* y
 x R y  and  y R* z => x R* z

I.e. elements are related by R* if they are related by R directly or through some sequence of intermediate related elements.

E.g. in graph theory, if R is the relation on nodes "has an edge leading to" then the transitive closure of R is the relation "has a path of zero or more edges to". See also Reflexive transitive closure.

Nearby terms:

transitivetransitive closuretransit networkTranslation Look-aside Buffer

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