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
A Unified Algorithm for Accelerating Edit-Distance Computation via Text-Compression
TL;DR: The classical four-russians technique can be incorporated into the SLP edit-distance scheme, giving us a simple $\Omega(\lg N)$ speed-up in the case of arbitrary scoring functions, for any pair of strings.
Journal ArticleDOI
A grammar-based distance metric enables fast and accurate clustering of large sets of 16S sequences
TL;DR: This work introduces a fast and accurate clustering algorithm that relies on a grammar-based sequence distance and its statistical clustering quality is validated by clustering large datasets containing 16S rDNA sequences.
Journal ArticleDOI
Multivariate Multiscale Complexity Analysis of Self-Reproducing Chaotic Systems.
TL;DR: Multiscale multivariate permutation entropy (MMPE) and multiscales multivariate Lempel–Ziv complexity (MMLZC) are employed to analyze the complexity of those self-reproducing chaotic systems with one-directional and two- directional infinitely many chaotic attractors.
Proceedings ArticleDOI
At the Roots of Dictionary Compression: String Attractors
Dominik Kempa,Nicola Prezza +1 more
TL;DR: In this article, it was shown that the problem of finding a small set of positions capturing all distinct text's substrings is NP-complete for any constant ε > 0.
Journal ArticleDOI
Automatic evaluation of intrapartum fetal heart rate recordings: a comprehensive analysis of useful features.
TL;DR: Most of the features utilized for FHR characterization, including FIGO, HRV, nonlinear, wavelet, and time and frequency domain features, are investigated and assessed based on their statistical significance in the task of distinguishing the FHR into three FIGO classes.
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.