论文信息 - Automaticity of Double Sequences Generated by One-Dimensional Linear Cellular Automata - 字舞流文

Automaticity of Double Sequences Generated by One-Dimensional Linear Cellular Automata

Abstract We give a complete answer to the question whether a double sequence that is generated by a one-dimensional linear cellular automaton, and whose states are integers modulo m , is k -automatic or not.

Heinz-Otto Peitgen | Jean-Paul Allouche | Guentcho Skordev | Fritz von Haeseler | A. Petersen | H. Peitgen | J. Allouche | F. V. Haeseler | G. Skordev | A. Petersen

[1] G. Rauzy,et al. Suites algébriques, automates et substitutions , 1980 .

[2] I. Korec. Pascal triangles modulo n and modular trellises , 1990 .

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

[4] G. Hardy,et al. An Introduction to the Theory of Numbers , 1938 .

[5] Heinz-Otto Peitgen,et al. Fractal Patterns in Gaussian and Stirling Number Tables , 1998, Ars Comb..

[6] J.-P. Allouche,et al. Linear Cellular Automata, Finite Automata and Pascal's Triangle , 1996, Discret. Appl. Math..

[7] Michel Dekking,et al. Folds: III. More Morphisms , 1982 .

[8] Michel Dekking,et al. Folds - II. Symmetry disturbed , 1982 .

[9] C. Michaux,et al. LOGIC AND p-RECOGNIZABLE SETS OF INTEGERS , 1994 .

[10] Samuel Eilenberg,et al. Automata, languages, and machines. A , 1974, Pure and applied mathematics.

[11] S. Ginsburg,et al. Semigroups, Presburger formulas, and languages. , 1966 .

[12] L. E. Dickson. Introduction to the theory of numbers , 1933 .

[13] Jeffrey Shallit,et al. AUTOMATIC MAPS ON A SEMIRING WITH DIGITS , 1995 .