Simulation of Effective Subshifts by Two-dimensional Subshifts of Finite Type

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 aEuro broken vertical bar). 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 (Invent. Math. 176(1):131-167, 2009).