English

On the Minimal Uncompletable Word Problem

Formal Languages and Automata Theory 2010-04-26 v2

Abstract

Let S be a finite set of words over an alphabet Sigma. The set S is said to be complete if every word w over the alphabet Sigma is a factor of some element of S*, i.e. w belongs to Fact(S*). Otherwise if S is not complete, we are interested in finding bounds on the minimal length of words in Sigma* which are not elements of Fact(S*) in terms of the maximal length of words in S.

Cite

@article{arxiv.1002.1928,
  title  = {On the Minimal Uncompletable Word Problem},
  author = {Gabriele Fici and Elena V. Pribavkina and Jacques Sakarovitch},
  journal= {arXiv preprint arXiv:1002.1928},
  year   = {2010}
}

Comments

5 pages; added references, corrected typos

R2 v1 2026-06-21T14:45:12.684Z