MODULO THREE PROBLEM WITH A CELLULAR AUTOMATON SOLUTION

Hao Xu, K. M. Lee and H. F. Chau ()
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Hao Xu: Department of Physics, University of Hong Kong, Pokfulam Road, Hong Kong, China
K. M. Lee: Department of Physics, University of Hong Kong, Pokfulam Road, Hong Kong, China
H. F. Chau: Department of Physics, University of Hong Kong, Pokfulam Road, Hong Kong, China

International Journal of Modern Physics C (IJMPC), 2003, vol. 14, issue 03, 249-256

Abstract: An important global property of a bit string is the number of ones in it. It has been found that the parity (odd or even) of this number can be found by a sequence of deterministic, translational invariant cellular automata with parallel update in succession for a total ofO(N2)time. In this paper, we discover a way to check if this number is divisible by three using the same kind of cellular automata inO(N3)time. We also speculate that the method described here could be generalized to check if it is divisible by four and other positive integers.

Keywords: Cellular automaton; classifier system; discrete dynamical system; symbolic dynamics; 89.75.-k; 05.45.-a; 05.50.+q; 89.20.Ff (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1142/S0129183103004450

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