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In computer science, in particular in concurrency theory, a dependency relation is a binary relation on a finite domain Σ {\displaystyle \Sigma } , symmetric, and reflexive; i.e. a finite tolerance relation. That is, it is a finite set of ordered pairs D {\displaystyle D} , such that
In general, dependency relations are not transitive; thus, they generalize the notion of an equivalence relation by discarding transitivity.
Σ {\displaystyle \Sigma } is also called the alphabet on which D {\displaystyle D} is defined. The independency induced by D {\displaystyle D} is the binary relation I {\displaystyle I}
That is, the independency is the set of all ordered pairs that are not in D {\displaystyle D}. The independency relation is symmetric and irreflexive. Conversely, given any symmetric and irreflexive relation I {\displaystyle I} on a finite alphabet, the relation