Probabilistic representation of formal languages

The problem of assigning a probability to each string of a language L(G) generated by a grammar G is considered. Two methods are considered. One method assigns a probability to each production associated with G and the other assigns the probabilities on the basis of particular features of the language. Several necessary conditions that must be satisfied by these probability assignment techniques if they are to be consistant are presented. The problem of recognizing languages is also considered. It is shown that under some conditions it is possible to recognize a non finitestate language with a finite state acceptor if one is willing to accept a small probability of making an error.