  In this article we completely characterise constant length substitution
shifts which have an almost automorphic factor, or which have a bijective
substitution factor. Our approach is algebraic: we study these dynamical
properties in terms of a finite semigroup defined by the substitution. We
characterise the existence of almost automorphic factors in terms of Green's
R-relation, and the existence of bijective factors in terms of Green's
L-relation. Our results are constructive.
