Extensions on the Analysis of Elementary Cellular Automata with Process Graphs

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dc.contributor.authorKassardjian L.
dc.contributor.authorBalbi P.P.
dc.contributor.authorRuivo E.
dc.date.accessioned2025-04-01T06:37:09Z
dc.date.available2025-04-01T06:37:09Z
dc.date.issued2024
dc.description.abstract© 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.
dc.description.firstpage127
dc.description.issuenumber2-3
dc.description.lastpage155
dc.description.volume18
dc.identifier.doi10.32908/jca.v18.300824
dc.identifier.issnNone
dc.identifier.urihttps://dspace.mackenzie.br/handle/10899/40453
dc.relation.ispartofJournal of Cellular Automata
dc.rightsAcesso Restrito
dc.subject.otherlanguageCellular automata
dc.subject.otherlanguageDe Bruijn graph
dc.subject.otherlanguagelimit regular expression
dc.subject.otherlanguageprocess graph
dc.subject.otherlanguageregular language
dc.titleExtensions on the Analysis of Elementary Cellular Automata with Process Graphs
dc.typeArtigo
local.scopus.citations0
local.scopus.eid2-s2.0-85212589375
local.scopus.subjectCellular automatons
local.scopus.subjectDe Bruijn graphs
local.scopus.subjectElementary cellular automaton
local.scopus.subjectLimit behavior
local.scopus.subjectLimit regular expression
local.scopus.subjectLocal functions
local.scopus.subjectOne-dimensional
local.scopus.subjectProcess graphs
local.scopus.subjectRegular expressions
local.scopus.subjectTemporal evolution
local.scopus.updated2025-04-01
local.scopus.urlhttps://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85212589375&origin=inward
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