  Sequence comparison is a widely used computational technique in modern
molecular biology. In spite of the frequent use of sequence comparisons the
important problem of assigning statistical significance to a given degree of
similarity is still outstanding. Analytical approaches to filling this gap
usually make use of an approximation that neglects certain correlations in the
disorder underlying the sequence comparison algorithm. Here, we use the longest
common subsequence problem, a prototype sequence comparison problem, to
analytically establish that this approximation does make a difference to
certain sequence comparison statistics. In the course of establishing this
difference we develop a method that can systematically deal with these disorder
correlations.
