Errors in Regular Languages

Random occurrences of three types of errors in the input to a finite automaton are considered: an α error is a deletion of one symbol from the input string; a β error is an insertion of one extra symbol; and a δ error is a change of one symbol into another symbol. A method using operators for determining regular expressions defining error-corrupted strings is developed and is employed in the construction of a finite automaton, the outputs of which are stochastically generated by Bayes' Rule (with certain approximations) to take into account the frequencies with which strings appear as inputs and the probabilities of errors.