  We examine the NFA minimization problem in terms of atomic NFA's, that is,
NFA's in which the right language of every state is a union of atoms, where the
atoms of a regular language are non-empty intersections of complemented and
uncomplemented left quotients of the language. We characterize all reduced
atomic NFA's of a given language, that is, those NFA's that have no equivalent
states. Using atomic NFA's, we formalize Sengoku's approach to NFA minimization
and prove that his method fails to find all minimal NFA's. We also formulate
the Kameda-Weiner NFA minimization in terms of quotients and atoms.
