Extensions on the Analysis of Elementary Cellular Automata with Process Graphs
Tipo
Artigo
Data de publicação
2024
Periódico
Journal of Cellular Automata
Citações (Scopus)
0
Autores
Kassardjian L.
Balbi P.P.
Ruivo E.
Balbi P.P.
Ruivo E.
Orientador
Título da Revista
ISSN da Revista
Título de Volume
Membros da banca
Programa
Resumo
© 2024 Old City Publishing, Inc.Cellular automata (CAs) are homogeneous dynamical systems discrete in time, space and state variables, with global states being updated by means of a local function acting of the neighbourhood of their consti-tuting parts. The family of elementary CAs (ECAs) is made up by the one-dimensional binary CAs with three next-nearest neighbours. Any one-dimensional CA’s local function can be represented by a De Bruijn graph, in which connected pairs of nodes represent its possible neigh-bourhoods and the edges connecting them, the corresponding state tran-sitions. De Bruijn graphs are specific kinds of process graphs, which are non-deterministic finite automata that can be used to represent the CA’s regular language obtained at each finite instant of time in the CA’s temporal evolution. The complexity of a process graph is defined defined in terms of the number of its nodes and edges. Previous works already analysed process graphs of ECAs’ temporal evolution and their com-plexities, as well as their growth patterns over several iterations and limit behaviour. Here, we advance on what is known in this respect for ECAs, expanding previously known complexity data on the evolution of process graphs for various rules, inferring the limit behaviour of two rules and developing a direct way of constructing the process graph associated to a specific rule at any finite number of time steps.
Descrição
Palavras-chave
Assuntos Scopus
Cellular automatons , De Bruijn graphs , Elementary cellular automaton , Limit behavior , Limit regular expression , Local functions , One-dimensional , Process graphs , Regular expressions , Temporal evolution