Facteurs des suites de Rudin-Shapiro généralisées

\Integrating" paperfolding sequences yields generalized Rudin-Shapiro sequences. We study the factors (subwords) of these sequences, giving an (optimal) property of \half-synchronization" and a uniform linear bound for the recurrence function. We also study the powers occurring in these sequences, and we show that the language consisting of all their factors is not contextfree.

[1]  Mireille Bousquet-Mélou,et al.  Canonical Positions for the Factors in Paperfolding Sequences , 1994, Theor. Comput. Sci..

[2]  Jean Berstel,et al.  A Geometric Proof of the Enumeration Formula for Sturmian Words , 1993, Int. J. Algebra Comput..

[3]  Jean-Paul Allouche,et al.  The number of factors in a paperfolding sequence , 1992, Bulletin of the Australian Mathematical Society.

[4]  Jean-Paul Allouche,et al.  Generalized Rudin-Shapiro sequences , 1991 .

[5]  Filippo Mignosi Sturmian Words and Ambigous Context-Free Languages , 1990, Int. J. Found. Comput. Sci..

[6]  S. Dulucq,et al.  On the factors of the Sturmian sequences , 1990 .

[7]  Jeffrey Shallit,et al.  The Ring of k-Regular Sequences , 1990, Theor. Comput. Sci..

[8]  Dominique Gouyou-Beauchamps,et al.  Sur les Facteurs des Suites de Sturm , 1990, Theor. Comput. Sci..

[9]  M. Queffélec,et al.  Une nouvelle propriété des suites de Rudin-Shapiro , 1987 .

[10]  J. Kahane Some Random Series of Functions , 1985 .

[11]  Gérald Tenenbaum,et al.  Dimension des courbes planes, papiers plies et suites de Rudin-Shapiro , 1981 .

[12]  Helmut Prodinger,et al.  Infinite 0-1-sequences without long adjacent identical blocks , 1979, Discret. Math..

[13]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[14]  L. Carlitz,et al.  Note on the Shapiro polynomials , 1970 .

[15]  Walter Rudin,et al.  Some theorems on Fourier coefficients , 1959 .

[16]  F. H. Young Transformations of Fourier coefficients , 1952 .

[17]  H. Shapiro,et al.  Extremal problems for polynomials and power series , 1951 .