Subshifts of the three dot system

Abstract

An example of a two-dimensional subshift is the set of arrays $\{x_{(i,j)}:(i,j)\in\mathbb{Z}^2\}$ of zeros and ones for which $x_{(i,j)}+x_{(i+1,j)}+x_{(i,j+1)}=0$ for each $i,j\in\mathbb{Z}$, where addition is taken modulo 2. There are two shift operators, the horizontal shift and the vertical shift. This subshift is called the Ledrappier example or the three dot dynamical system. In this paper we give an internal description of all transitive subshifts for which one of the shift operators is sofic in the usual one-dimensional sense.