General Form of an HMM
An HMM is specified by a five-tuple (S, K, ?, A, B) where S and K are the set of states and the output alphabet, and ?, A, B are the probabilities for the initial state, state transitions, and symbol emissions, respectively.
Given a specification of an HMM, we can simulate the running of a Markov process and produce an output sequence using the algorithm shown on the next page.
More interesting than a simulation, however, is assuming that some set of data was generated by a HMM, and then being able to calculate probabilities and probable underlying state sequences.