Sequence complexity as a test for cryptographic systems
Proceedings of CRYPTO 84 on Advances in cryptology
Average Profile of the Generalized Digital Search Tree and the Generalized Lempel--Ziv Algorithm
SIAM Journal on Computing
Information-Theoretic Limitations of Formal Systems
Journal of the ACM (JACM)
Data compression with long repeated strings
Information Sciences: an International Journal - Dictionary based compression
Compression in the presence of shared data
Information Sciences: an International Journal - Dictionary based compression
On the average redundancy rate of the Lempel—Ziv code with the k-error protocol
Information Sciences: an International Journal - Dictionary based compression
Estimating the Entropy Rate of Spike Trains via Lempel-Ziv Complexity
Neural Computation
User modeling for personalized Web search with self-organizing map: Research Articles
Journal of the American Society for Information Science and Technology
Discrete Applied Mathematics - 12th annual symposium on combinatorial pattern matching (CPM)
The Lempel-Ziv Complexity of Fixed Points of Morphisms
SIAM Journal on Discrete Mathematics
Grayscale two-dimensional lempel-ziv encoding
ICIAR'05 Proceedings of the Second international conference on Image Analysis and Recognition
On the Complexity of Finite Sequences
IEEE Transactions on Information Theory
A universal algorithm for sequential data compression
IEEE Transactions on Information Theory
Compression of individual sequences via variable-rate coding
IEEE Transactions on Information Theory
Causal coding of stationary sources and individual sequences with high resolution
IEEE Transactions on Information Theory
The Lempel-Ziv algorithm and message complexity
IEEE Transactions on Information Theory
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Investigations of complexity of sequences lead to important applications such as effective data compression, testing of randomness, discriminating between information sources and many others. In this paper we establish formulae describing the distribution functions of random variables representing the complexity of finite sequences introduced by Lempel and Ziv in 1976. It is known that this quantity can be used as an estimator of entropy. We show that the distribution functions depend affinely on the probabilities of the so-called ''exact'' sequences.