Merging Cellular Automata Rules to Optimise a Solution to the Modulo-n Problem

Understanding how the composition of cellular automata rules can perform predefined computations can contribute to the general notion of emerging computing by means of locally processing components. In this context, a solution has been recently proposed to the Modulo-n Problem, which is the determination of whether the number of 1-bits in a binary string is perfectly divisible by the positive integer n. Here, we show how to optimise that solution in terms of a reduction of the number of rules required, by means of a merging operation involving of the rules active state transitions. The potential for a more general usage of the merging operation is also addressed.