My PhD dissertation, supervised by Prof Michael Arbib at Stanford. Neighborhood reduction theorems are derived in this interest, and several simple computation-universal CA are presented. Conditions for computation-universality of a CA are investigated, and, in particular, the conjecture that unbounded but boundable propagation in a space is a sufficient condition is refuted. However, CA are shown to be inherently faster than interactive acceptors. No 4, 456-459, Apr 1971 Abstract .
L is proved.
The minimum state set for this class is shown to be the binary state set. The temporal costs, if any, of structural complexity trade-offs are also studied. It is demonstrated that any linear time cost can be eliminated and, in fact, a speed-up by arbitrary positive integer factor k can be attained at an increased structural cost. Jul 1971 Abstract . Neighborhood reduction and state-set reduction are shown to be particularly simple in this special theory, and one dimension is proved to be sufficient for computation universality.