Equivalence of state representations for hidden Markov models

In this paper we consider the following problem for (quasi) hidden Markov models: given a minimal (quasi) hidden Markov model, what can be said about the set of all equivalent (quasi) hidden Markov models of the same order. A distinction is made between Mealy and Moore type of hidden Markov models. A complete solution is presented for the quasi HMM case. For quasi Mealy models, there exists already a description of the set of equivalent models. In this paper, we prove that for minimal quasi Moore models, the set of equivalent models consists of only one element (up to a permutation of the states). Finally, we present some initial results for the positive HMM case and show a motivating simulation example.