A weak equivalence between shifts of finite type

Abstract

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⊂A Z , T⊂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.