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Simulation of Effective Subshifts by Two-dimensional Subshifts of Finite Type (1602.06095v1)
Published 19 Feb 2016 in math.DS, cs.DM, and cs.FL
Abstract: In this article we study how a subshift can simulate another one, where the notion of simulation is given by operations on subshifts inspired by the dynamical systems theory (factor, projective subaction...). There exists a correspondence between the notion of simulation and the set of forbidden patterns. The main result of this paper states that any effective subshift of dimension d -- that is a subshift whose set of forbidden patterns can be generated by a Turing machine -- can be obtained by applying dynamical operations on a subshift of finite type of dimension d + 1 -- a subshift that can be defined by a finite set of forbidden patterns. This result improves Hochman's [Hoc09].