Periodicity problem of substitutions over ternary alphabets
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 4, pp. 747-762.

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

DOI : 10.1051/ita:2007057
Classification : 11B85, 68R15
Mots-clés : periodicity, substitution
@article{ITA_2008__42_4_747_0,
     author = {Tan, Bo and Wen, Zhi-Ying},
     title = {Periodicity problem of substitutions over ternary alphabets},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {747--762},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {4},
     year = {2008},
     doi = {10.1051/ita:2007057},
     mrnumber = {2458705},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ita:2007057/}
}
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
SP  - 747
EP  - 762
VL  - 42
IS  - 4
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/ita:2007057/
DO  - 10.1051/ita:2007057
LA  - en
ID  - ITA_2008__42_4_747_0
ER  - 
%0 Journal Article
%A Tan, Bo
%A Wen, Zhi-Ying
%T Periodicity problem of substitutions over ternary alphabets
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2008
%P 747-762
%V 42
%N 4
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/ita:2007057/
%R 10.1051/ita:2007057
%G en
%F ITA_2008__42_4_747_0
Tan, Bo; Wen, Zhi-Ying. Periodicity problem of substitutions over ternary alphabets. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 4, pp. 747-762. doi : 10.1051/ita:2007057. http://archive.numdam.org/articles/10.1051/ita:2007057/

[1] N.J. Fine and H.S. Wilf, Uniqueness theorem for periodic functions. Proc. Amer. Math. Soc. 16 (1965) 109-114. | MR | Zbl

[2] T. Harju and M. Linna, On the periodicity of morphisms on free monoids. RAIRO-Theor. Inf. Appl. 20 (1986) 47-54. | Numdam | MR | Zbl

[3] T. Head, Fixed languages and the adult language of 0L schemes. Int. J. Comput. Math. 10 (1981) 103-107. | MR | Zbl

[4] B. Lando, Periodicity and ultimate periodicity of D0L systems. Theor. Comput. Sci. 82 (1991) 19-33. | MR | Zbl

[5] M. Lothaire, Combinatorics on Words. Encyclopedia of Mathematics and its Applications, Vol. 17, Addison-Wesley (1983). | MR | Zbl

[6] J. Pansiot, Decidability of periodicity for infinite words. RAIRO-Theor. Inf. Appl. 20 (1986) 43-46. | Numdam | MR | Zbl

[7] G. Rozenberg and A. Salomaa, The Mathematical Theory of L Systems. Academic Press, New York (1980). | MR | Zbl

[8] P. Séébold, An effective solution to the D0L periodicity problem in the binary case. EATCS Bull. 36 (1988) 137-151. | Zbl

Cité par Sources :