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arXiv · 1104.0388

On Non-Complete Sets and Restivo's Conjecture

Vladimir V. Gusev·Elena V. Pribavkina
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Abstract

A finite set S of words over the alphabet A is called non-complete if Fact(S*) is different from A*. A word w in A* - Fact(S*) is said to be uncompletable. We present a series of non-complete sets S_k whose minimal uncompletable words have length 5k^2 - 17k + 13, where k > 3 is the maximal length of words in S_k. This is an infinite series of counterexamples to Restivo's conjecture, which states that any non-complete set possesses an uncompletable word of length at most 2k^2.

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Vladimir V. Gusev, Elena V. Pribavkina. 2011-04-03. On Non-Complete Sets and Restivo's Conjecture. https://arxiv.org/abs/1104.0388

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