Cellular automata complexity trade-offs*

TLDR: 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.

Abstract: The general theory of cellular automata is investigated with special attention to structural complexity. In particular, simulation of cellular automata by cellular automata is used to make explicit trade-off relationships between neighborhood size and state-set cardinality. A minimum neighborhood template with d + 1 elements is established for the class of d -dimensional cellular automata. 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.