Lecture Notes in Mathematics Volume 1342, 1988, pp 374-424
Date: 28 Sep 2006

Decidability of shift equivalence

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Shift equivalence is the relation between matrices A, B that matrices R, S exist with RA=BR, AS=SA, SR=An, RS=Bn, n∈Z. We prove decidability in all cases of shift equivalence over Z + reducing it to congruences, inequalities, and determinant conditions on a C such that R0C is a desired Z shift equivalence, where R0 is a given shift equivalence over Q. Congruences are only modulo primes occurring to bounded powers in the determinant. We find generators for a group in which other primes are invertible, and for cosets of this group and reduce modulo some m.