Finite state automata representing two-dimensional subshifts

Authors:
Nataa Jonoska;Joni B. Pirnot
Affiliations:
University of South Florida, Department of Mathematics, Tampa, FL 33620, USA;Manatee Community College, Department of Mathematics, Bradenton, FL 34207, USA
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

A new type of two-dimensional automaton has been defined to recognize a class of two-dimensional 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 two-dimensional 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.