Parity Problem With A Cellular Automaton Solution

Details Parity Problem With A Cellular Automaton Solution Parity Problem With A Cellular Automaton Solution

2001-02-21

arxiv.org/abs/nlin/0102026v2

Nonlinear Sciences

Cellular Automata and Lattice Gases

Revtex, 4 pages, final version accepted by Phys.Rev.E

Scientific paper

10.1103/PhysRevE.64.026702

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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