TY - JOUR
T1 - On the classifiability of cellular automata
AU - Baldwin, John T.
AU - Shelah, Saharon
PY - 2000/1/6
Y1 - 2000/1/6
N2 - 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 Ap,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.
AB - 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 Ap,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.
KW - Cellular automata
KW - Classification
KW - Turing machines
UR - http://www.scopus.com/inward/record.url?scp=0000311275&partnerID=8YFLogxK
U2 - 10.1016/S0304-3975(99)00042-0
DO - 10.1016/S0304-3975(99)00042-0
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AN - SCOPUS:0000311275
SN - 0304-3975
VL - 230
SP - 117
EP - 129
JO - Theoretical Computer Science
JF - Theoretical Computer Science
IS - 1-2
ER -