Partial reversibility of one-dimensional cellular automata

dc.contributor.authorde Castro Correa R.
dc.contributor.authorde Oliveira P.P.B.
dc.description.abstract© IFIP International Federation for Information Processing 2016.Reversibility is the property of very special cellular automata rules by which any path traversed in the configuration space can be traversed back by its inverse rule. Expanding this context, the notion of partial reversibility has been previously proposed in the literature, as an attempt to refer to rules as being more or less reversible than others, since some of the paths of non-reversible rules could be traversed back. The approach was couched in terms of a characterisation of the rule’s pre-image pattern, that is, the number of pre-images of a rule for all configurations up to a given size, and their relative lexicographical ordering used to classify the rules in terms of their relative partial reversibility. Here, we reassess the original definition and define a measure that represents the reversibility degree of the rules, also based on their pre-image patterns, but now relying on the probability of correctly reverting each possible cyclic, finite length configuration, up to a maximum size. As a consequence, it becomes possible to look at partial reversibility in absolute terms, and not relatively to other rules, as well to infer the reversibility degrees for arbitrary lattice sizes, even in its limit to infinity. All the discussions are restricted to the elementary space, but are also applicable to any one-dimensional rule space.
dc.relation.ispartofLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
dc.rightsAcesso Aberto
dc.subject.otherlanguageElementary space
dc.subject.otherlanguageOne-dimensional cellular automata
dc.subject.otherlanguagePartial reversibility
dc.subject.otherlanguagePre-image Pattern
dc.subject.otherlanguageReversibility degree
dc.subject.otherlanguageReversible rule
dc.titlePartial reversibility of one-dimensional cellular automata
dc.typeArtigo de evento
local.scopus.subjectElementary space
local.scopus.subjectPartial reversibility
local.scopus.subjectPre images
local.scopus.subjectReversibility degree
local.scopus.subjectReversible rule