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The ambiguity of primitive words

  • H. Petersen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 775)

Abstract

A word is primitive if it is not a proper power of a shorter word. We prove that the set Q of primitive words over an alphabet is not an unambiguous context-free language. This strengthens the previous result that Q cannot be deterministic context-free. Further we show that the same holds for the set L of Lyndon words. We describe 2DPDA accepting Q and L which imply efficient decidability on the RAM model of computation and we analyse the number of comparisons required for deciding Q. Finally we give a new proof showing a related language not to be context-free, which only relies on properties of semi-linear and regular sets.

Keywords

Normal Order Formal Language Theory Proper Power Lyndon Word Primitive Word 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • H. Petersen
    • 1
  1. 1.Fachbereich InformatikUniversität HamburgDeutschland

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