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In this case, the elements of the set are usually referred to as executions of the system.

The name prefix order stems from the prefix order on words, which is a special kind of substring relation and, because of its discrete character, a tree.

Formal definition

A prefix order is a binary relation "<=" over a set P which is antisymmetric, transitive, reflexive, and downward total, i.e., for all a, b, and c in P, we have that:

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