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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Efficient universal lossless data compression algorithms based on a greedy sequential grammar transform. I. Without context models
En-hui Yang,John C. Kieffer +1 more
TL;DR: It is proved that for some nonstationary sources, the proposed context-dependent algorithms can achieve better expected redundancies than any existing CFG-based codes, including the Lempel-Ziv (1978) algorithm, the multilevel pattern matching algorithm, and the context-free algorithms in Part I of this series of papers.
Journal ArticleDOI
A novel multiscale nonlinear ensemble leaning paradigm for carbon price forecasting
TL;DR: The empirical analysis demonstrates that the proposed model can achieve higher level and directional predictions and higher robustness and seems an advanced approach for predicting the high nonstationary, nonlinear and irregular carbon price.
Journal ArticleDOI
Using Literal and Grammatical Statistics for Authorship Attribution
TL;DR: It turns out that the frequencies of occurrences of letter pairs and pairs of grammatical classes in a Russian text are rather stable characteristics of an author and, apparently, they could be used in disputed authorship attribution.
Journal ArticleDOI
Numerical evaluation of algorithmic complexity for short strings
Jean-Paul Delahaye,Hector Zenil +1 more
TL;DR: An alternative method that combines several theoretical and experimental results to numerically approximate the algorithmic Kolmogorov-Chaitin complexity of all deterministic 2-symbol Turing machines with up to four states is described.
Journal ArticleDOI
Integrated Information Increases with Fitness in the Evolution of Animats
Jeffrey A. Edlund,Nicolas Chaumont,Nicolas Chaumont,Arend Hintze,Arend Hintze,Christof Koch,Christof Koch,Christof Koch,Giulio Tononi,Christoph Adami,Christoph Adami +10 more
TL;DR: It is suggested that the correlation of fitness with information integration and with processing measures implies that high fitness requires both information processing as well as integration, but that information integration may be a better measure when the task requires memory.
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.
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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.
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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.