Williams’s conjecture is false for reducible subshifts
K. H. Kim, F.W. Roush · Journal of the American Mathematical Society · 1992
We show that for two subshifts of finite type having exactly two irreducible components, strong shift equivalence is not the same as shift equivalence. This refutes the Williams conjecture [ W ] [{\text {W}}] in the reducible case. The irreducible case remains an open problem.