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Automata accepting primitive words

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Abstract

LeA be an automaton whose set of inputs equalsX (|X|≧2) and whose cardinality of the set of states equalsn (n≧2), and letQ be the set of all primitive words overX. ByT(A) we denote the language accepted byA. In this paper, we give the following results:

  1. (1)

    T(A)⋔Q≠ ⊘ if and only ifA accepts a primitive wordy withlg(y)≦3n−3, wherelg(y) means the length ofy.

  2. (2)

    |T(A)⋔Q|=∞ if and only ifA accepts a primitive wordy withn≦lg(y)≦3n−3, where |T(A)⋔Q| means the cardinality ofT(A)⋔Q.

Moreover, we deal with the case |T(A)⋔Q|<∞ and obtain upper bounds on the cardinalities ofT(A)⋔Q and of some language related toT(A).

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References

  1. Hopcroft, J. E. and T. D. Ullman,Formal Languages and Their Relation to Automata, Addison-Wesley, Massachusetts, (1976)

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  2. Katsura, M. and S. S. Yu,Shortest Length of Primitive Words Accepted by Automata, in preparation.

  3. Lothaire, M.,Combinatrics on Words, Addison-Wesley, Massachusetts, (1983).

    MATH  Google Scholar 

  4. Shyr, H. J. and G. Thierrin,Disjunctive Languages and Codes, Fundamentals of Computation Theory, Proceedings of the 1977 Inter. FCT-Conference, Poznan, Poland, Lecture Notes in Computer Science, No. 56, Springer-Verlag (1977) 171–176.

  5. Shyr, H. J.,Free Monoids and Languages, Lecture Notes, Department of Mathematics, Soochow University, Taipei, Taiwan (1979).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Faculty of Science, Kyoto Sangyo University, 603, Kyoto, Japan

    M. Ito & M. Katsura

  2. Institute of Applied Mathematics, National Chung-Hsing University, 400, Taichung, Taiwan

    H. J. Shyr & S. S. Yu

Authors
  1. M. Ito
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  2. M. Katsura
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  3. H. J. Shyr
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  4. S. S. Yu
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Communicated by Boris M. Schein

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Ito, M., Katsura, M., Shyr, H.J. et al. Automata accepting primitive words. Semigroup Forum 37, 45–52 (1988). https://doi.org/10.1007/BF02573122

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  • DOI: https://doi.org/10.1007/BF02573122

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