Simple computation-universal cellular spaces and self-reproduction

Authors:
Alvy Ray Smith
Affiliations:
-
Venue:
SWAT '68 Proceedings of the 9th Annual Symposium on Switching and Automata Theory (swat 1968)
Year:
1968

Citing 0
Cited 3

Simple Computation-Universal Cellular Spaces

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Abstract

Cellular spaces computationally equivalent to any given Turing machine are exhibited which are simple in the sense that each cell has only a small number of states and a small neighborhood. Neighborhood reduction theorems are derived in this interest, and several simple computationuniversal cellular spaces are presented. Conditions for computation-universality of a cellular space are investigated, and, in particular, the conjecture that unbounded but boundable propagation in a space is a sufficient condition is refuted. Finally, the computation-universal spaces derived in the study are used to introduce, via recursive function theory, examples of simple self-reproducing universal Turing machine configurations in one and two dimensions.