ABSTRACT
The purpose of these remarks is not, unfortunately, to solve Williams' problem but rather to clarify it In [4], Williams introduced two equivalence relations for non–negative, integral, irreducible matrices. The first, strong shift equivalence, was shown to be a necessary and sufficient condition for the associated shifts of finite type to be topologically conjugate. The second, shift equivalence, is implied by strong shift equivalence and has the advantage of being much more tractable – indeed, Kim and Roush [1] have shown that the relation is decidable. However, no one has succeeded in proving (or disproving) that shift equivalence implies strong shift equivalence.
