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, EP n , 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.
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© 2006 Springer-Verlag Berlin Heidelberg
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Doğanaksoy, A., Göloğlu, F. (2006). On Lempel-Ziv Complexity of Sequences. In: Gong, G., Helleseth, T., Song, HY., Yang, K. (eds) Sequences and Their Applications – SETA 2006. SETA 2006. Lecture Notes in Computer Science, vol 4086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11863854_15
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DOI: https://doi.org/10.1007/11863854_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44523-4
Online ISBN: 978-3-540-44524-1
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