Pastel
PastelSys
Algorithms
Graph algorithms
Functional transitive closure

Functional transitive closure

Let $X$ be a set, $(Y, +)$ be a commutative monoid, $f : X -> Y$ , and $< subset X^2$ . Then the transitive closure $f^+ : X -> Y$ of $f$ is given by

$f^+(x) = +{f(x'): x <^+ x'},$

where $<^+$ is the transitive closure of $<$ (i.e. the intersection of all transitive relations containing $<$ ). We define $+emptyset = I$ , where $I$ is the identity of the monoid, and $+{y} = y$ , for all $y in Y$ .

Files

Functional transitive closure

Files

Concepts for the functional transitive closure

Testing for functional transitive closure

Transitive closure module

Transitive closure of a function