Modulo Three Problem With A Cellular Automaton Solution
Cellular Automata and Lattice Gases
2009-11-07 v1 Computational Complexity
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.
Cite
@article{arxiv.nlin/0207032,
title = {Modulo Three Problem With A Cellular Automaton Solution},
author = {Hao Xu and K. M. Lee and H. F. Chau},
journal= {arXiv preprint arXiv:nlin/0207032},
year = {2009}
}
Comments
10 pages in revtex 4.0, using amsfonts