A weak equivalence between shifts of finite type

We introduce the following notion of weak equivalence between shifts of finite type. Two shifts of finite type S and T are equivalent if and only if there are finite alphabets A and B and sliding block maps f from A(Z) to B-Z and g from B-Z to A(Z) such that S subset of A(Z), T subset of B-Z, S = f(-1) (T) and T = g(-1) (S). We give a necessary condition for this equivalence and we show how to decide the equivalence when the shifts are given by finite circular codes. (C) 2002 Elsevier Science (USA). All rights reserved.