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On a conjecture of J. Shallit

  • Session 17: Formal Languages III
  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1256))

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Abstract

We solve a conjecture of J. Shallit related to the automaticity function of a unary language, or equivalently to the first occurrence function in a symbolic sequence. The answer is negative: the conjecture is false, but it can be corrected by changing the constant involved. The proof is based on a study of paths in the Rauzy graphs associated with the sequence.

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References

  1. J.-P. Allouche and M. Bousquet-Mélou, On the conjectures of Rauzy and Shallit for infinite words, Comment. Math. Univ. Carolinae36 (1995), 705–711.

    Google Scholar 

  2. P. Arnoux and G. Rauzy, Représentation géométrique des suites de complexité 2n+1, Bull. Soc. Math. Prance119 (1991), 199–215.

    Google Scholar 

  3. J. Cassaigne, A proof of Rauzy's conjecture through an exhaustive study of factor graphs. In preparation.

    Google Scholar 

  4. J. Cassaigne, Facteurs spéciaux et complexité, Bull. Belg. Math. Soc. 4 (1997), 67–88. Special issue: Actes des Journées Montoises d'Informatique Théorique 1994.

    Google Scholar 

  5. M. Morse and G. A. Hedlund, Symbolic dynamics II: Sturmian trajectories, Amer. J. Math. 61 (1940), 1–42.

    Google Scholar 

  6. C. Pomerance, J. M. Robson, AND J. Shallit, Automaticity II: Descriptional complexity in the unary case, Theoret. Comput. Sci. To appear.

    Google Scholar 

  7. G. Rauzy, Suites à termes dans un alphabet fini, Sém. de Théorie des Nombres de Bordeaux, 1982–1983, 25.01–25.16.

    Google Scholar 

  8. G. Rote, Sequences with subword complexity 2n, J. Number Th.46 (1994), 196–213.

    Article  Google Scholar 

  9. J. Shallit and Y. Breitbart, Automaticity I: Properties of a measure of descriptional complexity, J. Comput. System Sci.53 (1996), 10–25.

    Article  Google Scholar 

  10. A. M. Vershik, Locally transversal symbolic dynamics, St. Petersburg Math. J.6 (1995), 529–540.

    Google Scholar 

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Authors and Affiliations

  1. Institut de Mathématiques de Luminy, Case 930, F-13288, Marseille Cedex 9, France

    Julien Cassaigne

Authors
  1. Julien Cassaigne
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Editor information

Pierpaolo Degano Roberto Gorrieri Alberto Marchetti-Spaccamela

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© 1997 Springer-Verlag Berlin Heidelberg

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Cassaigne, J. (1997). On a conjecture of J. Shallit. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds) Automata, Languages and Programming. ICALP 1997. Lecture Notes in Computer Science, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63165-8_223

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  • DOI: https://doi.org/10.1007/3-540-63165-8_223

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63165-1

  • Online ISBN: 978-3-540-69194-5

  • eBook Packages: Springer Book Archive

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