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Parity problem with a cellular automaton solution

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 11 Jul 2001Embargo end date: 01 Jan 2001 China (People's Republic of) English Publisher:American Physical Society (APS)Journal:Physical Review E, volume 64 (issn: 1063-651X, eissn: 1095-3787, Copyright policy )
Authors: Lee, KM; Xu, H; Chau, HF;

doi: 10.1103/physreve.64.026702 , 10.48550/arxiv.nlin/0102026

pmid: 11497739

arXiv: http://arxiv.org/abs/nlin/0102026

handle: 10722/43328

Parity problem with a cellular automaton solution

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.

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

Country
China (People's Republic of)
Related Organizations
Keywords

FOS: Computer and information sciences, Statistical Mechanics (cond-mat.stat-mech), Theorem Proving, Cellular Automata and Lattice Gases (nlin.CG), Binary Sequences, FOS: Physical sciences, Computational Complexity (cs.CC), Nonlinear Sciences - Adaptation and Self-Organizing Systems, Computer Science - Computational Complexity, Boundary Conditions, Nonlinear Sciences - Cellular Automata and Lattice Gases, Adaptation and Self-Organizing Systems (nlin.AO), Problem Solving, Condensed Matter - Statistical Mechanics

  • BIP!
    Impact byBIP!
    citations
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 17
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    		 Average
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
17
Average
Top 10%
Average
Green