Modulo Three Problem With A Cellular Automaton Solution

Details Modulo Three Problem With A Cellular Automaton Solution Modulo Three Problem With A Cellular Automaton Solution

2002-07-18

arxiv.org/abs/nlin/0207032v1

Nonlinear Sciences

Cellular Automata and Lattice Gases

10 pages in revtex 4.0, using amsfonts

Scientific paper

10.1142/S0129183103004450

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 of O(N^2) time. In this paper, we discover a way to check if this number is divisible by three using the same kind of cellular automata in O(N^3) time. We also speculate that the method described here could be generalized to check if it is divisible by four and other positive integers.

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