On Non-complete Sets and Restivo's Conjecture
نویسندگان
چکیده
A finite set S of words over the alphabet Σ is called noncomplete if Fact(S∗) 6= Σ∗. A word w ∈ Σ∗ \ Fact(S∗) is said to be uncompletable. We present a series of non-complete sets Sk whose minimal uncompletable words have length 5k − 17k+13, where k ≥ 4 is the maximal length of words in Sk. 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.
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تاریخ انتشار 2011