Abstract
This entry contains a formalization of hidden Markov models [3] based
on Johannes Hölzl's formalization of discrete time Markov chains
[1]. The basic definitions are provided and the correctness of two
main (dynamic programming) algorithms for hidden Markov models is
proved: the forward algorithm for computing the likelihood of an
observed sequence, and the Viterbi algorithm for decoding the most
probable hidden state sequence. The Viterbi algorithm is made
executable including memoization. Hidden markov models have various
applications in natural language processing. For an introduction see
Jurafsky and Martin [2].