JP Journal of Algebra, Number Theory and Applications
Volume 11, Issue 2, Pages 169 - 183
(August 2008)
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CHARACTERIZING TWO-DIMENSIONAL SOFIC SYSTEMS
Abdulkafi Al-Refaei (Malaysia), Syahida Che Dzul-Kifli (Malaysia) and Mohd. Salmi Md. Noorani (Malaysia)
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Abstract: 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. |
Keywords and phrases: subshifts of finite type, sofic system and semi-group. |
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