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Characterizing two-dimensional sofic systems. (English) Zbl 1228.37010

Summary: In this paper, three different ways of characterizing two-dimensional sofic systems are presented. The first characterization is as a symbolic factor of a subshift of finite type. The second is in terms of two-dimensional follower set and the third is in terms of two-dimensional semi-groups. The relationship between two-dimensional sofic systems and subshift of finite type is also showed. We prove that, as in the one-dimensional case, every subshift of finite type is a sofic system, but the converse is not necessarily true. Some examples are presented to illustrate this relationship.

MSC:

37B10 Symbolic dynamics
54H20 Topological dynamics (MSC2010)
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