Journal ArticleDOI
Combinatorial foundations of information theory and the calculus of probabilities
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The growing role of finite mathematics is discussed in this paper, where the definition of complexity, regularity and randomness, and the stability of frequencies of infinite random sequences are discussed, as well as relative complexity and quantity of information.Abstract:
CONTENTS ??1. The growing role of finite mathematics ??2. Information theory ??3. The definition of complexity ??4. Regularity and randomness ??5. The stability of frequencies ??6. Infinite random sequences ??7. Relative complexity and quantity of information ??8. Barzdin's theorem ??9. ConclusionReferencesread more
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An Introduction to Kolmogorov Complexity and Its Applications
Ming Li,Paul M. B. Vitányi +1 more
TL;DR: The book presents a thorough treatment of the central ideas and their applications of Kolmogorov complexity with a wide range of illustrative applications, and will be ideal for advanced undergraduate students, graduate students, and researchers in computer science, mathematics, cognitive sciences, philosophy, artificial intelligence, statistics, and physics.
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The Google Similarity Distance
TL;DR: A new theory of similarity between words and phrases based on information distance and Kolmogorov complexity is presented, which is applied to construct a method to automatically extract similarity, the Google similarity distance, of Words and phrases from the WWW using Google page counts.
Journal ArticleDOI
Akaike's information criterion and recent developments in information complexity
TL;DR: This paper presents some recent developments on a new entropic or information complexity (ICOMP) criterion of Bozdogan for model selection and operationalizes the general form of ICOMP based on the quantification of the concept of overall model complexity in terms of the estimated inverse-Fisher information matrix.
Journal ArticleDOI
What is a complex system
TL;DR: In this paper, the authors present a taxonomy of standard measures of complexity from the scientific literature, and offer their own list of necessary conditions as a characterization of complexity, and conclude that these conditions are qualitative and may not be jointly sufficient for complexity.
Journal ArticleDOI
Computational Mechanics: Pattern and Prediction, Structure and Simplicity
TL;DR: This paper showed that the causal-state representation of ∈-machine is the minimal one consistent with accurate prediction and established several results on ∈machine optimality and uniqueness and on how ∆-machines compare to alternative representations.
References
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Journal ArticleDOI
A Formal Theory of Inductive Inference. Part II
TL;DR: Four ostensibly different theoretical models of induction are presented, in which the problem dealt with is the extrapolation of a very long sequence of symbols—presumably containing all of the information to be used in the induction.
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On the Length of Programs for Computing Finite Binary Sequences
TL;DR: An application to the problem of defining a patternless sequence is proposed in terms of the concepts here developed to study the use of Turing machines for calculating finite binary sequences.
Journal ArticleDOI
The complexity of finite objects and the development of the concepts of information and randomness by means of the theory of algorithms
A K Zvonkin,Leonid A. Levin +1 more
TL;DR: The present article is a survey of the fundamental results connected with the concept of complexity as the minimum number of binary signs containing all the information about a given object that are sufficient for its recovery (decoding).
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Logical basis for information theory and probability theory
TL;DR: A new logical basis for information theory as well as probability theory is proposed, based on computing complexity, according to a new approach to computing complexity.
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On the concept of a random sequence
TL;DR: In this paper, it was shown that the Merkmalraum of a Kollektiv can be represented as a random sequence of points of an appropriate space, and that this sequence satisfies certain conditions which correspond to those appearing in the description of the Kollektsiv as given.