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Modulo Three Problem With A Cellular Automaton Solution

Hao Xu·K. M. Lee·H. F. Chau
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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 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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Hao Xu, K. M. Lee, H. F. Chau. 2002-07-18. Modulo Three Problem With A Cellular Automaton Solution. https://doi.org/10.1142/s0129183103004450

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