53 research outputs found
Turing degrees of limit sets of cellular automata
Cellular automata are discrete dynamical systems and a model of computation.
The limit set of a cellular automaton consists of the configurations having an
infinite sequence of preimages. It is well known that these always contain a
computable point and that any non-trivial property on them is undecidable. We
go one step further in this article by giving a full characterization of the
sets of Turing degrees of cellular automata: they are the same as the sets of
Turing degrees of effectively closed sets containing a computable point
Slopes of 3-dimensional Subshifts of Finite Type
International audienceIn this paper we study the directions of periodicity of three-dimensional subshifts of finite type (SFTs) and in particular their slopes. A configuration of a subshift has a slope of periodicity if it is periodic in exactly one direction, the slope being the angles of the periodicity vector. In this paper, we prove that any Σ_2 set may be realized as a a set of slopes of an SFT
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