Reduction factors in finite automata with application to nonlinear filters

We examine the reduction factors achieved in finite automata describing several important classes of stack filters. It has been shown that finite automata and Markov Chain theory can be used to compute certain statistical properties of stack filters. However, if the automaton is not state-minimal, the solution may be intractable, which is the motivation for this work. Formulae for the number of states in state-minimal automata are presented.