Morphisms Between Sofic Shift Spaces
The lower entropy factor problem asks for necessary and sufficient conditions for the existence of a factor map from a (mixing) sofic shift space onto another (mixing) sofic subshift of lower entropy. The problem was posed by Mike Boyle in 1984. It remains an open problem, but the present thesis gives a re-formulation which can be used to effectively decide the question for a larger class of sofic shifts than all previous results. In addition, the methods are used to make progress on the corresponding embedding problem which asks for necessary and sufficient conditions for the existence of an embedding of a (mixing) sofic shift into another (mixing) sofic shift of larger entropy.
Thesis advisor: Klaus Thomsen