In mathematics and computer science, a dependency relation is a binary relation that is finite, symmetric, and reflexive; i.e. a finite tolerance relation. That is, it is a finite set of ordered pairs, such that
- If then (symmetric)
- If is an element of the set on which the relation is defined, then (reflexive)
In general, dependency relations are not transitive; thus, they generalize the notion of an equivalence relation by discarding transitivity.
Let denote the alphabet of all the letters of . Then the independency induced by is the binary relation
That is, the independency is the set of all ordered pairs that are not in . Clearly, the independency is symmetric and irreflexive.
The pairs and, or the triple (with induced by ) are sometimes called the concurrent alphabet or the reliance alphabet.
The pairs of letters in an independency relation induce an equivalence relation on the free monoid of all possible strings of finite length. The elements of the equivalence classes induced by the independency are called traces, and are studied in trace theory.
Read more about Dependency Relation: Examples
Famous quotes containing the words dependency and/or relation:
“Fate forces its way to the powerful and violent. With subservient obedience it will assume for years dependency on one individual: Caesar, Alexander, Napoleon, because it loves the elemental human being who grows to resemble it, the intangible element. Sometimes, and these are the most astonishing moments in world history, the thread of fate falls into the hands of a complete nobody but only for a twitching minute.”
—Stefan Zweig (18811942)
“You know there are no secrets in America. It’s quite different in England, where people think of a secret as a shared relation between two people.”
—W.H. (Wystan Hugh)