Representation of binary linear hidden Markov models in the form of algebraic Bayesian networks

Probabilistic graphical models including hidden Markov models and Bayesian networks are widespread in process modeling in such fields as speech recognition, information theory, machine translation and molecular biology. The goal of this work is toresearch of mutual relations between hidden Markov models and algebraic Bayesian networks. An algorithm to design a binary linear hidden Markov models as an algebraic Bayesian networks is suggested. The theorem about coincidence between probabilistic semantics is proven.