On initialization of finite state ρ/μ approximations of systems finite alphabets

In this paper, we revisit the construction of finite state ρ/μ approximations for systems over finite alphabets. We derive conditions under which the complexity of these approximations can be lowered by simplifying the initialization process, thus reducing the size (cardinality) of their state-space. For instances where this condition is not met, we propose an alternative construction of the approximation which has strictly fewer states than the existing construction.