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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 of the ACM (JACM) – Association for Computing Machinery
Published: Jul 1, 1971
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