Many aspects of defect theorems

  • Authors:

  • Tero Harju;Juhani Karhumäki

  • Affiliations:

  • Department of Mathematics, Turku Centre for Computer Science, University of Turku, Turku FIN-20014, Finland;Department of Mathematics, Turku Centre for Computer Science, University of Turku, Turku FIN-20014, Finland

  • Venue:
  • Theoretical Computer Science - Words, languages and combinatorics
  • Year:
  • 2004

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Abstract

We give a survey and a unified presentation of the defect theorem, its generalizations and recent aspects of interest. In its basic form, the defect theorem states that if a set of n words satisfies a nontrivial relation, then these words can be expressed simultaneously as products of at most n - 1 words. In other words, dependency of words causes a defect effect. There does not exist just one defect theorem, but several ones depending on the restrictions that are put to the n - 1 words. The defect theorem is closely related to equations of words, and in this way to the compactness theorem for systems of word equations.