Marzal and Vidal [8] recently considered the problem of computing the normalized edit distance between two strings, and reported experimental results which demonstrated the use of the measure to recognize handwritten characters. Their paper formulated the theoretical properties of the measure and developed two algorithms to compute it. In this short communication we shall demonstrate how this measure is related to an auxiliary measure already defined in the literature -- the inter-string constrained edit distance [10,11,15]. Since the normalized edit distance can be computed efficiently using the latter, the analytic and experimental results reported in [8] can be obtained just as accurately, but more efficiently, using the strategies presented here. I. PROBLEM STATEMENT In the comparison of text patterns, phonemes and biological macromolecules a question that has attracted much interest is that of quantifying the dissimilarity between strings. A review of such distance measures and ...

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 [14] 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 rec...

In this paper we present a foundational basis for optimal and information theoretic syntactic pattern recognition. We do this by developing a rigorous model, M * , for channels which permit arbitrarily distributed substitution, deletion and insertion syntactic errors. More explicitly, if A is any finite alphabet and A * the set of words over A, we specify a stochastically consistent scheme by which a string U A * can be transformed into any Y A * by means of arbitrarily distributed substitution, deletion and insertion operations. The scheme is shown to be Functionally Complete and stochastically consistent. Apart from the synthesis aspects, we also deal with the analysis of such a model and derive a technique by which Pr[Y|U], the probability of receiving Y given that U was transmitted, can be computed in cubic time using dynamic programming. One of the salient features of this scheme is that it demonstrates how dynamic programming can be applied to evaluate quantities involv...

. 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...

joserra63unavarra.e~ In this paper1, we introduce a fuzzy automaton for computing the similarity between pairs of strings and a genetic method for adjusting its parameters. The fuzzy automaton models the edit operations needed to transform any string into another one. The selection of appropriate fuzzy operations and fuzzy membership values for the transitions leads to improve the system performance for a particular application.