On Lempel-Ziv complexity of sequences

Doganaksoy A., Gologlu F.

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

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 4086
  • Basım Tarihi: 2006
  • Dergi Adı: SEQUENCES AND THEIR APPLICATIONS - SETA 2006
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, EMBASE, MathSciNet, Philosopher's Index, zbMATH
  • Sayfa Sayıları: ss.180-189
  • Anahtar Kelimeler: Lempel-Ziv complexity, randomness, X-2-statistics
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.