Finding The Sign Of A Function Value By Binary Cellular Automaton
<|reference_start|>Finding The Sign Of A Function Value By Binary Cellular Automaton: Given a continuous function $f(x)$, suppose that the sign of $f$ only has finitely many discontinuous points in the interval $[0,1]$. We show how to use a sequence of one dimensional deterministic binary cellular automata to determine the sign of $f(\rho)$ where $\rho$ is the (number) density of 1s in an arbitrarily given bit string of finite length provided that $f$ satisfies certain technical conditions.<|reference_end|>
@article{chau2001finding,
    title={Finding The Sign Of A Function Value By Binary Cellular Automaton},
    author={H. F. Chau, H. Xu, K. M. Lee, L. W. Siu and K. K. Yan},
    journal={arXiv preprint arXiv:nlin/0103057},
    year={2001},
    doi={10.1142/S0129183102003929},
    archivePrefix={arXiv},
    eprint={nlin/0103057},
    primaryClass={nlin.CG cond-mat cs.CC}
}