On Lempel-Ziv complexity of sequences

Doganaksoy A., Gologlu F.

SEQUENCES AND THEIR APPLICATIONS - SETA 2006, vol.4086, pp.180-189, 2006 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 4086
  • Publication Date: 2006
  • Journal Name: SEQUENCES AND THEIR APPLICATIONS - SETA 2006
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, EMBASE, MathSciNet, Philosopher's Index, zbMATH
  • Page Numbers: pp.180-189
  • Keywords: Lempel-Ziv complexity, randomness, X-2-statistics
  • Middle East Technical University Affiliated: Yes

Abstract

We derive recurrences for counting the number a(n, r) of sequences of length n with Lempel-Ziv complexity r, which has important applications, for instance testing randomness of binary sequences. We also give algorithms to compute these recurrences. We employed these algorithms to compute a(n, r) and expected value, EPn, of number of patterns of a sequence of length n, for relatively large n. We offer a randomness test based on the algorithms to be used for testing randomness of binary sequences. We give outputs of the algorithms for some n. We also provide results of the proposed test applied to the outputs of contestant stream ciphers of ECRYPT's eSTREAM.