On the distribution function of the complexity of finite sequences

Adiego, 2007, Lempel–Ziv compression of highly structured documents, Journal of the American Society for Information Science and Technology, 58, 461, 10.1002/asi.20496 Amigo, 2004, Estimating the entropy rate of spike trains via Lempel–Ziv complexity, Neural Computation, 16, 717, 10.1162/089976604322860677 Amigo, 2006, Variance estimators for the Lempel–Ziv entropy estimator, Chaos, 16, 043102, 10.1063/1.2347102 Bentley, 2001, Data compression with long repeated strings, Information Sciences, 135, 1, 10.1016/S0020-0255(01)00097-4 Brittain, 2005, Grayscale two-dimensional Lempel–Ziv encoding, Image Analysis and Recognition, LNCS, 3656, 328, 10.1007/11559573_41 Castelli, 2006, Bounds on expansion in LZ’77-like coding, IEEE Transactions on Information Theory, 52, 1974, 10.1109/TIT.2006.872848 Chaitin, 1974, Information-theoretic limitations of formal systems, Journal of the Association for Computing Machinery, 21, 403, 10.1145/321832.321839 Constantinescu, 2007, The Lempel–Ziv complexity of fixed points of morphisms, SIAM Journal on Discrete Mathematics, 21, 466, 10.1137/050646846 Factor, 2001, Compression in the presence of shared data, Information Sciences, 135, 29, 10.1016/S0020-0255(01)00099-8 Gilbert, 1992, The Lempel–Ziv algorithm and message complexity, IEEE Transactions on Information Theory, 38, 1839, 10.1109/18.165463 Ilie, 2004, Word complexity and repetitions in words, International Journal of Foundations of Computer Science, 15, 41, 10.1142/S0129054104002297 Klien, 2005, Parallel Lempel–Ziv coding, Discrete Applied Mathematics, 146, 180, 10.1016/j.dam.2004.04.013 Kolmogorov, 1965, Three approaches to the qualitative definition of information, Problems of Information Transmission, 1, 1 Lempel, 1976, On the complexity of finite sequences, IEEE Transactions on Information Theory, IT-22, 75, 10.1109/TIT.1976.1055501 Leung, 1985, Sequence complexity as a test for cryptographic systems, vol. 196, 468 Linder, 2006, Casual coding of stationary sources and individual sequences with high resolution, IEEE Transactions on Information Theory, 52, 662, 10.1109/TIT.2005.862075 Louchard, 1999, Average profile of the generalized digital search tree and the generalized Lempel–Ziv algorithm, SIAM Journal on Computation, 28, 904, 10.1137/S0097539796301811 Reznik, 2001, On the average redundancy rate of the Lempel–Ziv code with the k-error protocol, Information Sciences, 135, 57, 10.1016/S0020-0255(01)00101-3 G. Wignarajah, Complexity tests for statistical independence, M.S. Thesis, University Toledo, 1985. Ziv, 1977, A universal algorithm for sequential data compression, IEEE Transactions on Information Theory, 23, 337, 10.1109/TIT.1977.1055714 Ziv, 1978, Compression of individual sequences via variable rate coding, IEEE Transactions on Information Theory, 24, 530, 10.1109/TIT.1978.1055934 Ziv, 1990, Compression, tests for randomness and estimating the statistical model of individual sequences, 366