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Annual Symposium on Theoretical Aspects of Computer Science

STACS 1994: STACS 94 pp 679–690Cite as

The ambiguity of primitive words

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Part of the book series: Lecture Notes in Computer Science ((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.

Supported by the ESPRIT Basic Research Action WG 6317: Algebraic and Syntactic Methods in Computer Science (ASMICS 2)

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Authors and Affiliations

  1. Fachbereich Informatik, Universität Hamburg, Deutschland

    H. Petersen

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  1. H. Petersen
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Patrice Enjalbert Ernst W. Mayr Klaus W. Wagner

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© 1994 Springer-Verlag Berlin Heidelberg

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Petersen, H. (1994). The ambiguity of primitive words. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds) STACS 94. STACS 1994. Lecture Notes in Computer Science, vol 775. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57785-8_181

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  • DOI: https://doi.org/10.1007/3-540-57785-8_181

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57785-0

  • Online ISBN: 978-3-540-48332-8

  • eBook Packages: Springer Book Archive

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