Affiliations: Pós-Graduação em Engenharia Elétrica e Computação, Universidade Presbiteriana Mackenzie, São Paulo, SP - Brazil. [email protected], [email protected]
Correspondence:
[*]
Address for correspondence: Rua da Consolação 896, Consolação - 01302-907 São Paulo, SP - Brazil.
Note: [†] Thanks to IPM - Instituto Presbiteriano Mackenzie.
Note: [‡] Thanks to FAPESP - Fundação de Amparo à Pesquisa do Estado de São Paulo, MACKPESQUISA - Fundo Mackenzie de Pesquisa, and CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico.
Abstract: The understanding of how predefined computations can be attained by means of individual cellular automata rules, their spatial arrangements or their temporal sequences, is a key conceptual 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 arbitrary n.
Keywords: Cellular automata, emergent computation, rule composition, modulo-n problem, MODn, active state transitions, parity, classification, decision problem
