A variant of a finite state machine having a set of states, Q, an output alphabet, O, transition probabilities, A, output probabilities, B, and initial state probabilities, Π. The current state is not observable. Instead, each state produces an output with a certain probability (B). Usually the states, Q, and outputs, O, are understood, so an HMM is said to be a triple, (A, B, Π). Formal Definition: After Michael Cohen's lectures for CN760.

• A = (a_ij = P(q_j at t+1