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transitive closure

transitive closure of a transitive binary relation R. A relation R* defined as follows: x R* y

iff there exists a sequence x = x0,x1,…, xn = y

such that n > 0 and xi R xi+1, i = 0,1,2,…, n–1

It follows from the transitivity property that if x R y then x R* y

and that R is a subset of R*.

Reflexive closure is similar to transitive closure but includes the possibility that n = 0. Transitive and reflexive closures play important roles in parsing and compiling techniques and in finding paths in graphs.

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