## An effective algorithm for string correction using generalized edit distances -- I. Description of the . . . (1981)

Citations: | 18 - 10 self |

### BibTeX

@MISC{Kashyap81aneffective,

author = {R. L. Kashyap and B. J. Oommen},

title = {An effective algorithm for string correction using generalized edit distances -- I. Description of the . . . },

year = {1981}

}

### Years of Citing Articles

### OpenURL

### Abstract

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.

### Citations

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The Theory
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Citation Context ...en below. SIMPLIFIED VERSION OF ALGORITHM I. Input: (1) The dictionary H in terms of the sets H(‘) for all i<N, (the length of the longest word in H) and the tree structure of the FSM that accepts H. =-=(2)-=- The garbled string Y. Output: The string X+ E H which minimizes D( X/ Y). Method: D,Q.&/Y’O’)=O, where Y(O) = II. for K= 1 to M do if (2K<N,) S=2K else S=N,,, for every a E H(') do if (D,(a/Y(K-‘)) o... |

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Citation Context ... respectively. Further, for any XEH, let X, be its parent and xf its last symbol. Then Algorithm I can be seen to be equivalent to the procedure given below. SIMPLIFIED VERSION OF ALGORITHM I. Input: =-=(1)-=- The dictionary H in terms of the sets H(‘) for all i<N, (the length of the longest word in H) and the tree structure of the FSM that accepts H. (2) The garbled string Y. Output: The string X+ E H whi... |

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Relative Frequency of English Speech Sounds
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Citation Context ...The error probabilities in this case are higher than the average error rates considered by Neuhoff [ 121, and the length of the words is about the average length of the 1021 most common English words =-=[23]-=-. Even in this case, we obtain that 99.840% of the erroneous strings will not contain two consecutive deletions. Hence, if the noisy channel obeys Assumption ii, the algorithm presented here can be us... |

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Citation Context ...nd Y(‘-i) respectively. In Sec. II, we define the distance D(X/Y) and obtain an explicit expression for it. In the next section we prove its recursive properties. Using dynamic programming procedures =-=[4]-=-, we proceed to show how X+ can be obtained recursively. The fact that the structure of this FSM that accepts H can be represented as a tree, is used in the companion paper [ 181 to study the computat... |

1 | A faster ~go~thm computing string edit distances, .I. Cornput. System Sri - Masek, Paterson - 1980 |

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