Detecting Regularities on Grammar-Compressed Strings

We solve the problems of detecting and counting various forms of regularities in a string represented as a Straight Line Program (SLP). Given an SLP of size n that represents a string s of length N , our algorithm compute all runs and squares in s in O(nh) time and O(n) space, where h is the height of the derivation tree of the SLP. We also show an algorithm to compute all gapped-palindromes in O(nh+ gnh logN) time and O(n) space, where g is the length of the gap. The key technique of the above solution also allows us to compute the periods and covers of the string in O(nh) time and O(nh(n + log N)) time, respectively.