Multidimensional sofic shifts without separation and their factors

Abstract. For d ≥ 2 we exhibit mixing Zd shifts of finite type and sofic shifts with large entropy but poorly separated subsystems (in the sofic examples, the only minimal subsystem is a single point). These examples consequently have very constrained factors; in particular, no non-trivial full shift is a factor. We also provide examples to distinguish certain mixing conditions, and develop the natural class of “block gluing ” shifts. In particular, we show that block gluing shifts factor onto all full shifts of strictly smaller entropy. 1