Identifiability of hidden Markov processes and their minimum degrees of freedom

The identifiability problem of hidden Markov model is solved in the paper by means of a new linear algebraic consideration, which moreover reveals the minimum degrees of freedom of a given model. There exist subspaces which respectively represent transient part of ergodic part like ordinary finite-state Markov chain, and also exists a zero-subspace which is entirely different from that. The subspace corresponding to the minimum effective degrees of freedom is constructed. It is proved that there exists an isomorphism on that subspace when and only when two models are equivalent. [In Japanese.]