A generalization of discrete hidden Markov model and of Viterbi algorithm

The concepts of composite and basic symbols and composite and basic states are introduced and a generalized hidden Markov model is defined to allow variable length and depth of dependency. A recursive function is defined to compute the probability distribution of the transitions from basic or composite states to composite states. The Viterbi algorithm is generalized to compute the optimal state sequence given an observation sequence of length T with time cost of O (T×(max.(N, N_c))²), where N and N_c are the numbers of basic states and composite states respectively