Pattern recognition of strings containing traditional and generalized transposition errors

We study the problem of recognizing a string Y which is the noisy version of some unknown string X^* chosen from a finite dictionary, H. The traditional case which has been extensively studied in the literature is the one in which Y contains substitution, insertion and deletion errors. In this paper we present the first reported solution to the analytic problem of editing one string X to another, Y using these four edit operations. A scheme for obtaining the optimal edit operations has also been given. Both these solutions are optimal for the infinite alphabet case. Using these algorithms we present a syntactic pattern recognition scheme which corrects noisy text containing all these types of errors. The paper includes experimental results involving subdictionaries of the most common English words which demonstrate the superiority of our system over existing methods