Finite State Automata Representing Two-Dimensional Subshifts

A new type of two-dimensional automaton has been defined to recognize a class of twodimensional shifts of finite type having the property that every admissible block found within the related local picture language can be extended to a point of the subshift. Here it is shown that this automaton accurately represents the image of the represented twodimensional shift of finite type under a block code. It is then shown that these automata can be used to check for a certain type of two-dimensional transitivity in the factor language of the corresponding shift space and how this relates to periodicity in the two-dimensional case. The paper closes with a notion of ‘‘follower sets’’ that are used to reduce the size of the automata representing two-dimensional sofic shifts. © 2009 Elsevier B.V. All rights reserved.