Abstract
In a preceding article, we have studied the family of words derivated from characteristic Sturmian words. This study has lead to a new proof of the characterization of characteristic Sturmian words which are fixed points of morphisms. In this article, we extend this approach to all Sturmian words. The Sturmian words viewed as dynamical systems play an important role in obtaining this generalization.
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References
Allouche, J.P., Shallit, J.: Automatic sequences — Theory, applications, generalizations. Cambridge University Press, Cambridge (2003)
Araújo, I.M., Bruyère, V.: Sturmian words and a criterium by Michaux- Villemaire. In: Theoret. Comput. Sci (Appeared in Proceedings of the 4th International Conference on Words), Turku, Finland, pp. 83–94 (2003) (to appear)
Araújo, I.M., Bruyère, V.: Words derivated from Sturmian words. Theoret. Comput. Sci. (to appear)
Bernardi, D., Guerziz, A., Koskas, M.: Sturmian words: description and orbits, 30 pages (2004) (preprint)
Berstel, J.: Recent results in Sturmian words. In: Developments in language theory, II (Magdeburg, 1995), pp. 13–24. World Sci. Publishing, River Edge (1996)
Berstel, J., Séébold, P.: Morphismes de Sturm. Bull. Belg. Math. Soc. Simon Stevin 1(2), 175–189 (1994); Journées Montoises (Mons, 1992)
Crisp, D., Moran, W., Pollington, A., Shiue, P.: Substitution invariant cutting sequences. J. Théor. Nombres Bordeaux 5(1), 123–137 (1993)
Durand, F.: A characterization of substitutive sequences using return words. Discrete Mathematics 179, 89–101 (1998)
Holton, C., Zamboni, L.: Geometric realizations of substitutions. Bull. Soc. Math. France 126(2), 149–179 (1998)
Justin, J., Vuillon, L.: Return words in Sturmian words and episturmian words. Theor. Inform. Appl. 34(5), 343–356 (2000)
Komatsu, T., van der Poorten, A.J.: Substitution invariant Beatty sequences. Japan. J. Math (N.S.) 22(2), 349–354 (1996)
Lothaire, M.: Algebraic Combinatoric on Words. Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (2002); Theor. Inform. Appl. 34(5), 343–356 (2000)
Michaux, C., Villemaire, R.: Presburger arithmetic and recognizability of sets of natural numbers by automata: New proofs of Cobham’s and Semenov’s theorems. Annals of Pure and Applied Logic 77, 251–277 (1996)
Vuillon, L.: A characterization of Sturmian words by return words. European J. Combin. 22(2), 263–275 (2001)
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Araújo, I.M., Bruyère, V. (2005). Sturmian Words: Dynamical Systems and Derivated Words. In: De Felice, C., Restivo, A. (eds) Developments in Language Theory. DLT 2005. Lecture Notes in Computer Science, vol 3572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11505877_11
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DOI: https://doi.org/10.1007/11505877_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26546-7
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