Searching for Regularities in Weighted Sequences

In this paper we describe algorithms for finding regularities in weighted sequences. A weighted sequence is a sequence of symbols drawn from an alphabet Σ that have a prespecified probability of occurrence. We show that known algorithms for finding repeats in solid sequences may fail to do so for weighted sequences. In particular, we show that Crochemore’s algorithm for finding repetitions cannot be applied in the case of weighted sequences. However, one can use Karp’s algorithm to identify repeats of specific length. We also extend this algorithm to identify the covers of a weighted sequence. Finally, the implementation of Karp’s algorithm brings up some very interesting issues.