The Levenshtein-distance between two words is the minimal number of insertions, deletions or substitutions that are needed to transform one word into the other. Levenshtein-automata of degree n for a word W are defined as finite state automata that regognize the set of all words V where the Levenshtein-distance between V and W does not exceed n. We show how to compute, for any fixed bound n and any input word W , a deterministic Levenshtein-automaton of degree n for W in time linear in the length of W . Given an electronic dictionary that is implemented in the form of a trie or a finite state automaton, the Levenshtein-automaton for W can be used to control search in the lexicon in such a way that exactly the lexical words V are generated where the Levenshtein-distance between V and W does not exceed the given bound. This leads to a very fast method for correcting corrupted input words of unrestricted text using large electronic dictionaries. We then introduce a second method that avoids the explicit computation of Levenshtein-automata and leads to even improved eciency. We also describe how to extend both methods to variants of the Levenshtein-distance where further primitive edit operations (transpositions, merges and splits) may be used.

. We consider a problem which can greatly enhance the areas of cursive script recognition and the recognition of printed character sequences. This problem involves recognizing words/strings by processing their noisy subsequences. Let X * be any unknown word from a finite dictionary H. Let U be any arbitrary subsequence of X * . We study the problem of estimating X * by processing Y, a noisy version of U. Y contains substitution, insertion, deletion and generalized transposition errors -- the latter occurring when transposed characters are themselves subsequently substituted. We solve the noisy subsequence recognition problem by defining and using the constrained edit distance between X H and Y subject to any arbitrary edit constraint involving the number and type of edit operations to be performed. An algorithm to compute this constrained edit distance has been presented. Using these algorithms we present a syntactic Pattern Recognition (PR) scheme which corrects noisy tex...

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 (SID) errors. Although some work has been done to extend the traditional set of edit operations to include the straightforward transposition of adjacent characters 2 [LW75] the problem is unsolved when the transposed characters are themselves subsequently substituted, as is typical in cursive and typewritten script, in molecular biology and in noisy chain-coded boundaries. 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 reco...

This report presents a synoptic overview of Thue Systems. Thue Systems were introduced in the early 1900s by the Norwegian mathematician and logician Axel Thue. In this report the author suggests ways in which such systems can be used in pattern recognition.