This paper deals with the problem of estimating a transmitted string X, from the corresponding received string Y, which is a noisy version of X,. We assume that Y contains*any number of substitution, insertion, and deletion errors, and that no two consecutive symbols of X, were deleted in transmission. We have shown that for channels which cause independent errors, and whose error probabilities exceed those of noisy strings studied in the literature [ 121, at least 99.5 % of the erroneous strings will not contain two consecutive deletion errors. The best estimate X * of X, is defined as that element of H which minimizes the generalized Levenshtein distance D ( X/Y) between X and Y. Using dynamic programming principles, an algorithm is presented which yields X+ without computing individually the distances between every word of H and Y. Though this algorithm requires more memory, it can be shown that it is, in general, computationally less complex than all other existing algorithms which perform the same task. I.

e solutions `a ce probl`eme, on impose certaines conditions sur les expressions que l'on veut obtenir : ces derni`eres doivent retracer des propri'et'es des chaines qu'on a donn'ees, c'est-`adire que l'on cherche `a y exhiber une s'emantique inh'erente, ce qui sera d'efini formellement plus loin. Dans un univers o`u il n'y a pas de bruit d'observation et pas de modifications al'eatoires des objets, la reconnaissance exacte est possible. Malheureusement, dans une situation r'eelle, des alt'erations structurelles interviennent par suite d'un bruit attach'e `a toute observation ou mesure. Ceci conduit `a la reconnaissance tol'erante. Le mod`ele sous-jacent `a une telle reconnaissance pr'esume que la description structurelle id'eale d'un objet est modifi'ee al'eatoirement (suppression, ajout de parties, alt'eration de relations : : :). On suppose de plus que des descriptions structurelles peu modifi'ees sont de loin plus fr'equentes que des descriptions fortement modifi'ees

Grammar inference is the learning or model estimation required by any syntatic approach to pattern recognition. Given a sample of strings, the grammar inference procedure must infer the grammar which has generated these strings. Decidability questions have been discussed by Gold and they depend largely on the availability of all positive samples (known to have been generated by the grammar) and negative samples (strings not generated by the grammar). Restrictions on the grammar inference problem may apply: one may either constrain the set of positive samples or the set of negative samples, or the class of grammars where the solution has to be looked for, or even the complexity of the grammar inference procedure.