Characterisation of limit measures of higher dimensional cellular automata
Author
dc.contributor.author
Delacourt, Martín
Author
dc.contributor.author
Hellouin de Menibus, Benjamín
Admission date
dc.date.accessioned
2018-07-03T14:35:54Z
Available date
dc.date.available
2018-07-03T14:35:54Z
Publication date
dc.date.issued
2017
Cita de ítem
dc.identifier.citation
Theory of Computing Systems, Vol. 61(4): 1178-1213
es_ES
Identifier
dc.identifier.other
10.1007/s00224-017-9753-1
Identifier
dc.identifier.uri
https://repositorio.uchile.cl/handle/2250/149409
Abstract
dc.description.abstract
We 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 -> infinity. 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 CesA ro 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.
es_ES
Patrocinador
dc.description.sponsorship
FONDECYT Postdoctorado Proyecto
3130496
Basal project, Universidad de Chile
PFB-03 CMM