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Dependency relation

In computer science, in particular in concurrency theory, a dependency relation is a symmetric and reflexive binary relation on a finite domain ; i.e. a finite tolerance relation. That is, it is a finite set of ordered pairs , such thatIf then (symmetric) If , then (reflexive)

Examples
Given the alphabet \Sigma=\{a,b,c\}, a possible dependency relation is D = \{ (a,b),\, (b,a),\, (a,c),\, (c,a),\, (a,a),\, (b,b),\, (c,c) \}, see picture. The corresponding independency is I=\{(b,c),\,(c,b)\}. Then e.g. the symbols b,c are independent of one another, and e.g. a,b are dependent. The string a c b b a is equivalent to a b c b a and to a b b c a, but to no other string. ==References==
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