Crucial words and the complexity of some extremal problems for sets of prohibited words

Evdokimov, A. and Kitaev, Sergey (2004) Crucial words and the complexity of some extremal problems for sets of prohibited words. Journal of Combinatorial Theory Series A, 105 (2). pp. 273-289. ISSN 0097-3165

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Official URL: https://doi.org/10.1016/j.jcta.2003.12.003

Abstract

We introduce the notion 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 three special 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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Evdokimov, A. and Kitaev, Sergey

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Item metadata

Item type:	Article
ID code:	49115
Dates:	Date Event February 2004 Published 20 February 2004 Published Online
Keywords:	abelian squares, NP-completeness, crucial words, unavoidablity, avoidability, Electronic computers. Computer science, Discrete Mathematics and Combinatorics, Computational Theory and Mathematics, Theoretical Computer Science
Subjects:	Science > Mathematics > Electronic computers. Computer science
Department:	Faculty of Science > Computer and Information Sciences
Depositing user:	Pure Administrator
Date deposited:	06 Sep 2014 02:16
Last modified:	20 Jan 2021 21:25
Related URLs:	https://personal.cis.strath.ac.uk/sergey...
URI:	https://strathprints.strath.ac.uk/id/eprint/49115

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