Periodicity problem of substitutions over ternary alphabets

Bo Tan; Zhi-Ying Wen

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2008)

  • Volume: 42, Issue: 4, page 747-762
  • ISSN: 0988-3754

Abstract

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In this paper, we characterize the substitutions over a three-letter alphabet which generate a ultimately periodic sequence.

How to cite

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Tan, Bo, and Wen, Zhi-Ying. "Periodicity problem of substitutions over ternary alphabets." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 42.4 (2008): 747-762. <http://eudml.org/doc/245468>.

@article{Tan2008,
abstract = {In this paper, we characterize the substitutions over a three-letter alphabet which generate a ultimately periodic sequence.},
author = {Tan, Bo, Wen, Zhi-Ying},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {periodicity; substitution},
language = {eng},
number = {4},
pages = {747-762},
publisher = {EDP-Sciences},
title = {Periodicity problem of substitutions over ternary alphabets},
url = {http://eudml.org/doc/245468},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Tan, Bo
AU - Wen, Zhi-Ying
TI - Periodicity problem of substitutions over ternary alphabets
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2008
PB - EDP-Sciences
VL - 42
IS - 4
SP - 747
EP - 762
AB - In this paper, we characterize the substitutions over a three-letter alphabet which generate a ultimately periodic sequence.
LA - eng
KW - periodicity; substitution
UR - http://eudml.org/doc/245468
ER -

References

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  1. [1] N.J. Fine and H.S. Wilf, Uniqueness theorem for periodic functions. Proc. Amer. Math. Soc. 16 (1965) 109–114. Zbl0131.30203MR174934
  2. [2] T. Harju and M. Linna, On the periodicity of morphisms on free monoids. RAIRO-Theor. Inf. Appl. 20 (1986) 47–54. Zbl0608.68065MR849965
  3. [3] T. Head, Fixed languages and the adult language of 0L schemes. Int. J. Comput. Math. 10 (1981) 103–107. Zbl0472.68034MR645626
  4. [4] B. Lando, Periodicity and ultimate periodicity of D0L systems. Theor. Comput. Sci. 82 (1991) 19–33. Zbl0729.68038MR1112106
  5. [5] M. Lothaire, Combinatorics on Words. Encyclopedia of Mathematics and its Applications, Vol. 17, Addison-Wesley (1983). Zbl0514.20045MR675953
  6. [6] J. Pansiot, Decidability of periodicity for infinite words. RAIRO-Theor. Inf. Appl. 20 (1986) 43–46. Zbl0617.68063MR849964
  7. [7] G. Rozenberg and A. Salomaa, The Mathematical Theory of L Systems. Academic Press, New York (1980). Zbl0508.68031MR561711
  8. [8] P. Séébold, An effective solution to the D0L periodicity problem in the binary case. EATCS Bull. 36 (1988) 137–151. Zbl0678.68072

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