Covering problems from a formal language point of view

  • Authors:
  • Marcella Anselmo;Maria Madonia

  • Affiliations:
  • Dip. di Informatica ed Applicazioni, Università di Salerno, Baronissi, SA, Italy;Dip. di Matematica ed Informatica, Università di Catania, Catania, Italy

  • Venue:
  • DLT'03 Proceedings of the 7th international conference on Developments in language theory
  • Year:
  • 2003

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Abstract

We consider the formal language of all words that are 'covered' by words in a given language. This language is said cov-free when any word has at most one minimal covering over it. We study the notion of cov-freeness in relation with its counterpart in classical monoids and in monoids of zig-zag factorizations. In particular cov-freeness is characterized by the here introduced notion of cov-stability. Some more properties are obtained using this characterization. We also show that the series counting the minimal coverings of a word over a regular language is rational.