## Abstract

We address the problems of detecting and counting various forms of regularities in a string represented as a straight-line program (SLP) which is essentially a context free grammar in the Chomsky normal form. Given an SLP of size n that represents a string s of length N, our algorithm computes all runs and squares in s in O(n3h) time and O(n2) 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(n3h+gnhlogN) time and O(n2) space, where g is the length of the gap. As one of the main components of the above solution, we propose a new technique called approximate doubling which seems to be a useful tool for a wide range of algorithms on SLPs. Indeed, we show that the technique can be used to compute the periods and covers of the string in O(n2h) time and O(nh(n+log^{2}N)) time, respectively.

Original language | English |
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Journal | Information and Computation |

DOIs | |

Publication status | Accepted/In press - 2013 Oct 1 |

## Keywords

- Compressed string processing algorithms
- Gapped palindromes
- Runs
- Squares
- Straight-line programs (SLPs)

## ASJC Scopus subject areas

- Information Systems
- Computational Theory and Mathematics
- Theoretical Computer Science
- Computer Science Applications