Three complexity functions
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 1, pp. 67-76.

For an extensive range of infinite words, and the associated symbolic dynamical systems, we compute, together with the usual language complexity function counting the finite words, the minimal and maximal complexity functions we get by replacing finite words by finite patterns, or words with holes.

DOI : 10.1051/ita/2011126
Classification : 37B10, 68R15
Mots-clés : infinite words, symbolic dynamical systems, complexity
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Ferenczi, Sébastien; Hubert, Pascal. Three complexity functions. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 1, pp. 67-76. doi : 10.1051/ita/2011126. http://archive.numdam.org/articles/10.1051/ita/2011126/

[1] P. Alesssandri, Codages de rotations et basses complexités. Université Aix-Marseille II, Ph.D. thesis (1996).

[2] A. Avila and G. Forni, Weak mixing for interval exchange maps and translation flows, Ann. Math. (2) 165 (2007) 637 − 664. | MR | Zbl

[3] G. Castiglione, A. Restivo and S. Salemi, Patterns in words and languages. Discrete Appl. Math. 144 (2004) 237 − 246. | MR | Zbl

[4] J. Chaika, Topological mixing for some residual sets of interval exchange transformations. Preprint (2011).

[5] I.P. Cornfeld, S.V. Fomin and Y.G. Sinai, Ergodic theory. Translated from the Russian by A.B. Sosinski, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, New York 245 (1982) x+486. | MR | Zbl

[6] E.M. Coven and G.A. Hedlund, Sequences with minimal block growth. Math. Syst. Theory 7 (1973) 138-153. | MR | Zbl

[7] S. Ferenczi, Complexity of sequences and dynamical systems. Combinatorics and number theory (Tiruchirappalli, 1996). Discrete Math. 206 (1999) 145-154. | MR | Zbl

[8] T. Kamae, Uniform sets and complexity. Discrete Math. 309 (2009) 3738 − 3747. | MR | Zbl

[9] T. Kamae, Behavior of various complexity functions. Preprint (2011). | MR | Zbl

[10] T. Kamae and L. Zamboni, Sequence entropy and the maximal pattern complexity of infinite words. Ergod. Theory Dyn. Syst. 22 (2002) 1191-1199. | MR | Zbl

[11] T. Kamae and L. Zamboni, Maximal pattern complexity for discrete systems. Ergod. Theory Dyn. Syst. 22 (2002) 1201-1214. | MR | Zbl

[12] T. Kamae, H. Rao, B. Tan and Y.-M. Xue, Super-stationary set, subword problem and the complexity. Discrete Math. 309 (2009) 4417-4427. | MR | Zbl

[13] M.S. Keane, Non-ergodic interval exchange transformations. Israe"l J. Math. 26 (1977), 188-196. | MR | Zbl

[14] D. Lind and B. Marcus, An introduction to symbolic dynamics and coding. Cambridge University Press, Cambridge (1995) xvi+495. | MR | Zbl

[15] M. Morse and G.A. Hedlund, Symbolic dynamics. Amer. J. Math. 60 (1938) 815-866. | JFM | MR

[16] M. Morse and G.A. Hedlund, Symbolic dynamics II. Sturmian trajectories. Amer. J. Math. 62 (1940) 1 − 42. | JFM | MR

[17] N. Pytheas-Fogg, Substitutions in dynamics, arithmetics and combinatorics. Lect. Notes Math. 1794, edited by V. Berthé, S. Ferenczi, C. Mauduit and A. Siegel. Springer-Verlag, Berlin (2002). | MR | Zbl

[18] G. Rote, Sequences with subword complexity 2n. J. Number Theory 46 (1994) 196-213. | MR | Zbl

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