Abstract
A finite set S of words over the alphabet ∑ is called non-complete if Fact(S*) ≠ ∑*. A word w ∈ ∑* \ 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 ≥ 4 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. © 2011 Springer-Verlag.
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CITATION STYLE
Gusev, V. V., & Pribavkina, E. V. (2011). On non-complete sets and restivo’s conjecture. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6795 LNCS, pp. 239–250). https://doi.org/10.1007/978-3-642-22321-1_21
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