Finding overlaps within regular expressions with variable-length gaps

Regular expressions play an important role in various fields in computer science. However, handling many regular expressions in parallel requires huge computation resources. Therefore, it is necessary to find and eliminate overlapping regular expressions. In this paper, we consider a special type of regular expressions: expressions comprised of characters and variable-length gaps between such characters. Specifically, we propose a bit-parallel solution to determine whether the languages of two expressions X and Y with variable-length gaps have a common string. The time complexity of our algorithm is O (min (L_X ²|Σ|, L_X L_Y)/w) where Σ is the alphabet from which X and Y are drawn, L_X and L_Y are the lengths of the longest strings that respectively match X and Y, and w is the size of the computer word.