Digital Search Trees Again Revisited: The Internal Path Length Perspective
SIAM Journal on Computing
Asymptotic behavior of the Lempel-Ziv parsing scheme and digital search trees
Theoretical Computer Science - Special volume on mathematical analysis of algorithms (dedicated to D. E. Knuth)
Ziv-Lempel complexity for periodic sequences and its cryptographic application
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
On Independence and Sensitivity of Statistical Randomness Tests
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
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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.