ABSTRACT
This chapter introduces two interesting special topics: state reduction in Section 6.1, and hidden Markov chains in Section 6.2. State reduction is an iterative procedure which reduces a Markov chain to a smaller chain from which a solution to the original chain can be found. Roundoff error can be reduced when subtractions are avoided. A hidden Markov chain is one for which the states cannot be observed. When a hidden Markov chain enters a state, only an observation symbol, not the state itself, can be detected. Hidden Markov models have been constructed for various applications such as speech recognition and bioinformatics.
