Algorithms, Dynamic Programming, Machine Learning, Artificial Intelligence, Markov Models.
x[0], x[1], …, x[n−1], where x[0] is one of the s[i], x[1] is one of the s[i], and so on. Each state produces an observation, resulting in a sequence of observations y[0], y[1], …, y[n−1], where y[0] is one of the o[k], y[1] is one of the o[k], and so on. An HMM goes through a series of states,