Algebraic properties of cellular automata

Cellular automata are discrete dynamical systems, of simple construction but complex and varied behaviour. Algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata. The complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities. The systems are usually irreversible, and are found to evolve through transients to attractors consisting of cycles sometimes containing a large number of configurations.

[1]  E. T..  An Introduction to the Theory of Numbers , 1946, Nature.

[2]  E. F. Moore.  Machine Models of Self-Reproduction , 1962 .

[3]  Donald E. Knuth,et al.  fundamental algorithms , 1969 .

[4]  Periodic forest whose largest clearings are of size 3 , 1970, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[5]  Periodic forests of stunted trees , 1970, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[6]  Periodic forests whose largest clearings are of size n ≥ 4 , 1970, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[7]  F. MacWilliams,et al.  The Theory of Error-Correcting Codes , 1977 .

[8]  Joe W. Harris,et al.  Principles of Algebraic Geometry , 1978 .

[9]  Shoichi Noguchi,et al.  On Some Dynamical Properties of Finite Cellular Automaton , 1978, IEEE Transactions on Computers.

[10]  On the Cyclic Behavior of Random Transformations on a Finite Set. , 1981 .

[11]  Leonidas J. Guibas,et al.  String Overlaps, Pattern Matching, and Nontransitive Games , 1981, J. Comb. Theory A.

[12]  S. Wolfram.  Statistical mechanics of cellular automata , 1983 .

[13]  P. Grassberger.  New mechanism for deterministic diffusion , 1983 .

[14]  D. Lind.  Applications of ergodic theory and sofic systems to cellular automata , 1984 .

[15]  O. Antoine,et al.  Theory of Error-correcting Codes , 2022 .