Detecting regularities on grammar-compressed strings

Tomohiro I, Wataru Matsubara, Kouji Shimohira, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda, Kazuyuki Narisawa, Ayumi Shinohara

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


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 + gnh log N) 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 + log2 N)) time, respectively.

Original languageEnglish
Pages (from-to)74-89
Number of pages16
JournalInformation and Computation
Publication statusPublished - Feb 1 2015

All Science Journal Classification (ASJC) codes

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


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