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Crucial Words and the Complexity of Some Extremal Problems for Sets of Prohibited Words

A. Evdokimov·S. Kitaev
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Abstract

We introduced the notation of a set of prohibitions and give definitions of a complete set and a crucial word with respect to a given set of prohibitions. We consider 3 particular sets which appear in different areas of mathematics and for each of them examine the length of a crucial word. One of these sets is proved to be incomplete. The problem of determining lengths of words that are free from a set of prohibitions is shown to be NP-complete, although the related problem of whether or not a given set of prohibitions is complete is known to be effectively solvable.

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A. Evdokimov, S. Kitaev. 2002-05-20. Crucial Words and the Complexity of Some Extremal Problems for Sets of Prohibited Words. https://arxiv.org/abs/math/0205217

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