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In mathematics, especially order theory, a prefix ordered set generalizes the intuitive concept of a tree by introducing the possibility of continuous progress and continuous branching. Natural prefix orders often occur when considering dynamical systems as a set of functions from time to some phase space. 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.
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