• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.191-199
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• 1996

The strong shift equivalence of nonnegative integral square matrices is a necessary and sufficient condition for the topological conjugacy of topological Markov chains. In this paper we study the relation between strong shift equivalence and matrix conjugation.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.773-785
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• 1999

Shifts of finite type are represented by nonnegative integral square matrics, and conjugacy between two shifts of finite type is determined by strong shift equivalence between the representing nonnegative intergral square matrices. But determining strong shift equivalence is usually a very difficult problem. we develop splittings and amalgamations of nonnegative integral matrices, which are analogues of those of directed graphs, and show that two nonnegative integral square matrices are strong shift equivalent if and only if one is obtained from a higher matrix of the other matrix by a series of amalgamations.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.685-692
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• 1996

Subshifts of finite type can be classified by various equivalence relations. The most important equivalence relation is undoubtedly strong shift equivalence, i.e., conjugacy. In [W], R. F. Williams introduced shift equivalence which is weaker than conjugacy but still sensitive.