Fully Compressed Pattern Matching Algorithm for Balanced Straight-Line Programs

We consider a fully compressed pattern matching problem, where both text T and pattern P are given by its succinct representation, in terms of straight-line programs and its variant. The length of the text T and pattern P may grow exponentially with respect to its description size n and m, respectively. The best known algorithm for the problem runs in O(nm) time using O(nm) space. In this paper, we introduce a variant of straight-line programs, called balanced straight-line programs so that we establish a faster fully compressed pattern matching algorithm. Although the compression ratio of balanced straight-line programs may be worse than the original straight-line programs, they can still express exponentially long strings. Our algorithm runs in O(nm) time using O(nm) space.