On Lempel-Ziv complexity of sequences
Date
2006
Authors
Advisor
Instructor
Source Title
Sequences and Their Applications – SETA 2006
Print ISSN
0302-9743
Electronic ISSN
Publisher
Springer, Berlin, Heidelberg
Volume
4086
Issue
Pages
180 - 189
Language
English
Type
Conference Paper
Journal Title
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Volume Title
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. © Springer-Verlag Berlin Heidelberg 2006.
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Keywords
Lempel-Ziv complexity, Randomness, χ2-statistics, Algorithms, Binary sequences, Computation theory, Lempel-Ziv complexity, Randomness, Computational complexity