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Simple Computation-Universal Cellular Spaces

Simple Computation-Universal Cellular Spaces Simple Computation-Universal Cellular Spaces ALVY R A Y S M I T H I I I * New York University, The Bronx, New York ABSTRACT. The specialization of the t h e o r y of cellular spaces (cellular a u t o m a t a ) to those spaces which compute p a r t i a l recursive functions is presented. N e i g h b o r h o o d reduction and state-set reduction are shown to be p a r t i c u l a r l y simple in this special theory, and one dimension is proved to be sufficient for c o m p u t a t i o n universality. Several c o m p u t a t i o n - u n i v e r s a l cellular spaces (CUCS's) are exhibited which are simple in the sense t h a t each cell has only a small n u m b e r q of s t a t e s and a small n u m b e r p of neighbors. F o r example, a 1-dimensional CUCS http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the ACM (JACM) Association for Computing Machinery

Simple Computation-Universal Cellular Spaces

Journal of the ACM (JACM) , Volume 18 (3) – Jul 1, 1971

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Publisher
Association for Computing Machinery
Copyright
Copyright © 1971 by ACM Inc.
ISSN
0004-5411
DOI
10.1145/321650.321652
Publisher site
See Article on Publisher Site

Abstract

Simple Computation-Universal Cellular Spaces ALVY R A Y S M I T H I I I * New York University, The Bronx, New York ABSTRACT. The specialization of the t h e o r y of cellular spaces (cellular a u t o m a t a ) to those spaces which compute p a r t i a l recursive functions is presented. N e i g h b o r h o o d reduction and state-set reduction are shown to be p a r t i c u l a r l y simple in this special theory, and one dimension is proved to be sufficient for c o m p u t a t i o n universality. Several c o m p u t a t i o n - u n i v e r s a l cellular spaces (CUCS's) are exhibited which are simple in the sense t h a t each cell has only a small n u m b e r q of s t a t e s and a small n u m b e r p of neighbors. F o r example, a 1-dimensional CUCS

Journal

Journal of the ACM (JACM)Association for Computing Machinery

Published: Jul 1, 1971

References