String editing under a combination of constraints

Abstract

Let X and Y be any two strings of finite lengths N and M, respectively, over a finite alphabet. An edit distance between X and Y is defined as the minimum sum of elementary edit distances associated with edit operations of substitutions, deletions, and insertions needed to transform X to Y. In this paper, the problem of efficient computation of such a distance is considered under the assumption that the numbers of edit operations are limited and that the maximum lengths, F and G, of runs of deletions and insertions are given, respectively. Besides, the edit sequence is ordered in a sense that between every two successive runs of substitutions there can be either at most one run of deletions followed by at most one run of insertions or just one run of deletions or insertions. An algorithm is derived that computes the minimum edit distance associated with editing X to Y subject to the specified constraints. The algorithm requires O( NM min { N, M}) time and O( NM) space. Possible applications for the synchronization error-correcting codes and for the cryptanalysis of certain stream ciphers are also discussed.