On the classifiability of cellular automata

John T. Baldwin; Saharon Shelah

doi:10.1016/S0304-3975(99)00042-0

On the classifiability of cellular automata

John T. Baldwin^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

Based on computer simulations Wolfram presented in several papers conjectured classifications of cellular automata into four types. We show a natural formalization of his rate of growth suggestion does not provide a classification (even probabilistically) of all cellular automata: For any rational p, q, 0 ≤ p, q with p + q = 1, there is a cellular automata A_p,q which has probability p of being in class 3, probability q of being in class 4. We also construct an automata which grows monotonically at rate log t, rather than at a constant rate.

Original language	English
Pages (from-to)	117-129
Number of pages	13
Journal	Theoretical Computer Science
Volume	230
Issue number	1-2
DOIs	https://doi.org/10.1016/S0304-3975(99)00042-0
State	Published - 6 Jan 2000

Keywords

Cellular automata
Classification
Turing machines

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10.1016/S0304-3975(99)00042-0

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KW - Classification

KW - Turing machines

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On the classifiability of cellular automata

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