Characterisation of Limit Measures of Higher-Dimensional Cellular Automata

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dc.contributor.authorDelacourt, Martin
dc.contributor.authorHellouin de Menibus, Benjamin
dc.date.accessioned2023-11-15T15:46:35Z
dc.date.available2023-11-15T15:46:35Z
dc.date.issued2017-11
dc.descriptionIndexación: Scopuses
dc.description.abstractWe consider the typical asymptotic behaviour of cellular automata of higher dimension (≥2). That is, we take an initial configuration at random according to a Bernoulli (i.i.d) probability measure, iterate some cellular automaton, and consider the (set of) limit probability measure(s) as t → ∞. In this paper, we prove that limit measures that can be reached by higher-dimensional cellular automata are completely characterised by computability conditions, as in the one-dimensional case. This implies that cellular automata have the same variety and complexity of typical asymptotic behaviours as Turing machines, and that any nontrivial property in this regard is undecidable (Rice-type theorem). These results extend to connected sets of limit measures and Cesàro mean convergence. The main tool is the implementation of arbitrary computation in the time evolution of a cellular automata in such a way that it emerges and self-organises from a random configuration. © 2017, Springer Science+Business Media New York.es
dc.description.urihttps://www-sciencedirect-com.recursosbiblioteca.unab.cl/science/article/pii/S1062976917300686?via%3Dihub
dc.identifier.citationTheory of Computing Systems Volume 61, Issue 4, Pages 1178 - 12131 November 2017es
dc.identifier.doi10.1007/s00224-017-9753-1
dc.identifier.issn1432-4350
dc.identifier.urihttps://repositorio.unab.cl/xmlui/handle/ria/53973
dc.language.isoenes
dc.publisherSpringer New York LLCes
dc.rights.licenseCC BY 4.0 DEED
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/deed.es
dc.subjectCellular automataes
dc.subjectComputabilityes
dc.subjectLimit measurees
dc.subjectMultidimensionales
dc.subjectSymbolic dynamicses
dc.titleCharacterisation of Limit Measures of Higher-Dimensional Cellular Automataes
dc.typeArtículoes
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