Journal ArticleDOI
On the Complexity of Finite Sequences
A. Lempel,Jacob Ziv +1 more
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TLDR
A new approach to the problem of evaluating the complexity ("randomness") of finite sequences is presented, related to the number of steps in a self-delimiting production process by which a given sequence is presumed to be generated.Abstract:
A new approach to the problem of evaluating the complexity ("randomness") of finite sequences is presented. The proposed complexity measure is related to the number of steps in a self-delimiting production process by which a given sequence is presumed to be generated. It is further related to the number of distinct substrings and the rate of their occurrence along the sequence. The derived properties of the proposed measure are discussed and motivated in conjunction with other well-established complexity criteria.read more
Citations
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Proceedings ArticleDOI
Multistate Lempel-Ziv (MLZ) index interpretation as a measure of amplitude and complexity changes
TL;DR: A novel method to quantify amplitude and complexity variations in biomedical signals by means of the computation of the LZ coefficient using more than two quantification states, and with thresholds fixed and independent of the dynamic range or standard deviation of the analyzed signal: the Multistate Lempel-Ziv (MLZ) index.
Book ChapterDOI
Complexity and Universality in the Long-Range Order of Words
TL;DR: It is shown that a direct application of information theory leads to an entropy measure that can quantify semantic structures and extract keywords from linguistic samples, even without prior knowledge of the underlying language.
Journal ArticleDOI
Phase-only filtering for the masses (of DNA Data): a new approach to sequence alignment
TL;DR: The standard magnitude-and-phase cross correlation technique is compared with the lesser known but closely related phase-only cross correlation method and it is shown that for a periodic DNA sequence, the standard approach leads to significant sidelobes in the cross correlation, the magnitude of which increases with sequence length.
Journal ArticleDOI
Analysis of daily streamflow complexity by Kolmogorov measures and Lyapunov exponent
Dragutin T. Mihailović,Emilija Nikolić-Đorić,Ilija Arsenić,Slavica Malinović-Milićević,Vijay P. Singh,Tatijana Stosic,Borko Stosic +6 more
TL;DR: In this article, a set of Kolmogorov complexity measures (KC) and Lyapunov time (LT) were used to evaluate the effect of anthropogenic influences and climate change on streamflow variability.
Proceedings ArticleDOI
Motifs in Ziv-Lempel-Welch Clef
TL;DR: Adaptions and extensions of classical incremental ZL and ZLW paradigms are examined, in which the phrases used in compression are selected among suitably chosen motifs, defined here as strings of intermittently solid and wild characters that recur more or less frequently in the source textstring.
References
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Journal ArticleDOI
Three approaches to the quantitative definition of information
TL;DR: In this article, three approaches to the quantitative definition of information are presented: information-based, information-aware and information-neutral approaches to quantifying information in the context of information retrieval.
Journal ArticleDOI
The definition of random sequences
TL;DR: It is shown that the random elements as defined by Kolmogorov possess all conceivable statistical properties of randomness and can equivalently be considered as the elements which withstand a certain universal stochasticity test.
Journal ArticleDOI
Process complexity and effective random tests
TL;DR: A variant of the Kolmogorov concept of complexity which yields a common theory of finite and infinite random sequences and some concepts of effective tests which are proved to be equivalent are established.
Journal ArticleDOI
Information-Theoretic Limitations of Formal Systems
TL;DR: An attempt is made to apply information-theoretic computational complexity to meta-mathematics by measuring the difficulty of proving a given set of theorems, in terms of the number of bits of axioms that are assumed, and the size of the proofs needed to deduce the theoremic proofs.