Journal of the
Korean Mathematical Society JKMS

Shifts of finite type are represented by nonnegative integral square matrices, and conjugacy between two shifts of finite type is determined by strong shift equivalence between the representing nonnegative integral 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.

Keywords: symbolic dynamics, shift of finite type, strong shift equivalence, conjugacy, splitting, amalgamation, nonnegative integral matrix

MSC numbers: Primary 58F03, 54H20; Secondary 15A36, 60J10