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Classes of linear automata

Published online by Cambridge University Press:  19 September 2008

Robert H. Gilman
Affiliation:
Department of Mathematics, Stevens Institute of Technology, Hoboken, NJ 07030, USA and School of Mathematics, Institute for Advanced Study, Princeton NJ 08540, USA
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Abstract

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This paper discusses a division of one-dimensional cellular automata into classes which seem to correspond to different types of behaviour.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1987

References

REFERENCES

[1]Adler, R. L. & Marcus, B.. Topological Entropy and Equivalence of Dynamical Systems. Mem. Amer. Math. Soc. 20 (# 219), 1979.Google Scholar
[2]Riccia, G. Delia. Equicontinuous semi-flows (one-parameter semi-groups) on locally compact or complete metric spaces. Math. Systems Theory 4 (1970), 2934.CrossRefGoogle Scholar
[3]Farmer, D., Toffoli, T. & Wolfram, S. eds. Cellular Automata. North-Holland Pub. Co., Amsterdam 1984.Google Scholar
[4]Feller, W.. An Introduction to Probability Theory and its Applications, Vol. 1, first edition. J. Wiley, New York, 1950.Google Scholar
[5]Furstenberg, H.. Recurrence in Ergodic Theory and Combinatorial Number Theory. Princeton Univ. Press, Princeton, 1981.CrossRefGoogle Scholar
[6]Grassberger, P.. Chaos and diffusion in deterministic cellular automata. Physica 10D (1984), 5258 (reprinted in [3]).Google Scholar
[7]Hedlund, G. A.. Endomorphisms and automorphisms of the shift in dynamical systems. Math. Systems Theory 3 (1969), 320375.CrossRefGoogle Scholar
[8]Walters, P.. An Introduction to Ergodic Theory. Springer Verlag, New York, 1982.CrossRefGoogle Scholar
[9]Wolfram, S.. Universality and complexity in cellular automata. Physica 10D (1984), 135 (reprinted in [3]).Google Scholar
[10]Wolfram, S.. Computation theory of cellular automata. Comm. Math. Phys. 96 (1984), 1557.CrossRefGoogle Scholar