O problema MODn com composição de autômatos celulares unidimensionais: resolução e simplificações
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Tipo
Tese
Data de publicação
2016-08-24
Periódico
Citações (Scopus)
Autores
Martins, Claudio Luis de Meo
Orientador
Oliveira, Pedro Paulo Balbi de
Título da Revista
ISSN da Revista
Título de Volume
Membros da banca
Monteiro, Luiz Henrique Alves
Mendonça, José Ricardo Gonçalves de
Barbosa, Valmir Carneiro
Silva, Leandro Augusto da
Mendonça, José Ricardo Gonçalves de
Barbosa, Valmir Carneiro
Silva, Leandro Augusto da
Programa
Engenharia Elétrica
Resumo
The understanding of how the composition of cellular automata rules can perform prede
ned computations may contribute to the general notion of emerging computation by
means of locally processing components. In this context, we propose a solution to the
MODn Problem, which is the determination of whether the number of 1-bits in a binary
string is perfectly divisible by the positive integer n > 1. The solution is a composition of
one-dimensional cellular automata rules, i.e., the application of di erent rules on a lattice
with periodic boundary conditions, which are replaced after some iterations, and all of
them with maximum radius equal to n 1. In this work, the (XU; LEE; CHAU, 2003)
solution for MOD3 Problem (n = 3) is extended for any value of n, and the solution is
given for any lattice size N that is co-prime to n. In this generalised solution, the number
of iterations depends only on N, with O(N2). This solution relies upon two essential classes
of rules, that have been de ned herein: the Replacement rules, that replace a certain
amount of identical end bits on the lattice with the opposite value, and the Grouping
rules, that group isolated strings of identical and consecutive bits on the lattice, to larger
strings of the same bit value. Furthermore, we also show how the solution can be simpli-
ed in terms of a reduction on the number of required rules, by de ning some operations
that involve the rules' active state transitions, i.e., those that change the value of the
centre cell of the neighbourhood. To this end, we de ned the operations of Partitioning
(the separation of the active transitions of a rule in di erent rules), Joining (the union of
the all active transitions of di erent rules in the same rule), and Merging (the joining of
all active transitions of the rules involved, but removing some of them or even adding new
active transitions to get the desired adjustments. Using the same concepts and methodology, we proposed a x for the only rule that had been reported in the literature for
solving the MOD2 Problem, which is known as the Parity Problem.
Descrição
Palavras-chave
autômatos celulares , computação emergente , composição de regras , problema módulo-n , transições de estado ativas
Assuntos Scopus
Citação
MARTINS, Claudio Luis de Meo. O problema MODn com composição de autômatos celulares unidimensionais: resolução e simplificações. 2016. 93 f. Tese (Engenharia Elétrica) - Universidade Presbiteriana Mackenzie, São Paulo .