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Parity Problem With A Cellular Automaton Solution

K. M. Lee·Hao Xu·H. F. Chau
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Abstract

The parity of a bit string of length $N$ is a global quantity that can be efficiently compute using a global counter in ${O} (N)$ time. But is it possible to find the parity using cellular automata with a set of local rule tables without using any global counter? Here, we report a way to solve this problem using a number of $r=1$ binary, uniform, parallel and deterministic cellular automata applied in succession for a total of ${O} (N^2)$ time.

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K. M. Lee, Hao Xu, H. F. Chau. 2001-05-03. Parity Problem With A Cellular Automaton Solution. https://doi.org/10.1103/physreve.64.026702

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