Sequential Circuit Output Probabilities From Regular Expressions

This paper presents a number of methods for finding sequential circuit output probabilities using regular expressions. Various classes of regular expressions, based on their form, are defined and it is shown how to easily find multistep transition probabilities directly from the regular expressions. A new procedure for finding steady-state probabilities is given which proceeds either from a regular expression or a state diagram description. This procedure is based on the concept of synchronization of the related machine, and is useful for those problems where synchronization sequences exist. In the cases where these techniques can be utilized, substantial savings in computation can be realized. Furthermore, application to other areas such as multinomial Markov processes is immediate.