Abstract
The understanding of how predefined computations can be attained by means of individ- ual cellular automata rules, their spatial arrangements or their temporal sequences, is a key concep- tual underpinning in the general notion of emergent computation. In this context, here we construct a solution to the MODn problem, which is the determination of whether the number of 1-bits in a cyclic binary string is perfectly divisible by the integer n > 1. Our solution is given for any lattice size N that is co-prime to n, and relies upon a set of one-dimensional rules, with maximum radius of n 1, organised in a temporal sequence. Although the simpler cases of the problem for n = 2 and n = 3 have been addressed in the literature, this is the first account on the general case, for arbitraryn.
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