Solving Classical String Problems an Compressed Texts

How to solve string problems, if instead of input string we get only program generating it? Is it possible to solve problems faster than just "generate text + apply classical algorithm"? In this paper we consider strings generated by straight-line programs (SLP). These are programs using only assignment operator. We show new algorithms for equivalence, pattern matching, finding periods and covers, computing fingerprint table on SLP-generated strings. From the other hand, computing the Hamming distance is NP-hard. Main corollary is an $O(n2*m)$ algorithm for pattern matching in LZ-compressed texts