A multiway system is a kind of substitution system in which multiple states are permitted at any stage. This accommodates rule systems in which there is more than one possible way to perform an update. A simple example is a string substitution system. For instance, take the rules {A B->A, B A->B} and the initial condition A B A. There are two choices for how to proceed. Applying the first rule yields the evolution A B A t o A A, while applying the second rule yields the evolution A B A->A B->A. So at the first step, there is a single state ({A B A}), at the second step there are two states {A A, A B}, and at the third step there is a single state {A}.
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