State splitting and state merging in probabilistic finite state automata

Probabilistic finite state automata (PΓSA) are constructed from symbol sequences for modeling the behavior of dynamical systems. This paper presents construction of finite history automata from symbol sequences; such automata, called D-Markov machines, are structurally simple and computationally efficient. The construction procedure is based on: (i) state splitting that generates symbol blocks of different lengths according to their relative importance; and (ii) state merging that assimilates histories from symbol blocks leading to the same symbolic behavior. A metric on probability distribution of symbol blocks is introduced for trade-off between modeling performance and the number of PFSA states. These algorithms have been tested by two examples.