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Abstract

We develop a natural matrix formalism for state splittings and amalgamations of higher-dimensional subshifts of finite type which extends the common notion of strong shift equivalence of ${\mathbb Z}^+$-matrices. Using the decomposition theorem every topological conjugacy between two ${\mathbb Z}^d$-shifts of finite type can thus be factorized into a finite chain of matrix transformations acting on the transition matrices of the two subshifts. Our results may be used algorithmically in computer explorations on topological conjugacies and in the search for new conjugacy invariants.