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Increasing Kolmogorov complexity
 In Proceedings of the 22nd Symposium on Theoretical Aspects of Computer Science
, 2005
"... classification: Kolmogorov complexity, computational complexity 1 ..."
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classification: Kolmogorov complexity, computational complexity 1
Kolmogorov complexity and computational complexity
 Complexity of Computations and Proofs. Quaderni di Matematica
, 2004
"... We describe the properties of various notions of timebounded Kolmogorov complexity and other connections between Kolmogorov complexity and computational complexity. 1 ..."
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Cited by 3 (0 self)
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We describe the properties of various notions of timebounded Kolmogorov complexity and other connections between Kolmogorov complexity and computational complexity. 1
Kolmogorov Complexity Arguments in Combinatorics
 J. COMB. TH., SERIES A
, 1994
"... The utility of a Kolmogorov complexity method in combinatorial theory is demonstrated by several examples. ..."
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Cited by 6 (3 self)
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The utility of a Kolmogorov complexity method in combinatorial theory is demonstrated by several examples.
An introduction to Kolmogorov Complexity and its Applications: Preface to the First Edition
, 1997
"... This document has been prepared using the L a T E X system. We thank Donald Knuth for T E X, Leslie Lamport for L a T E X, and Jan van der Steen at CWI for online help. Some figures were prepared by John Tromp using the xpic program. The London Mathematical Society kindly gave permission to reproduc ..."
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Cited by 2138 (120 self)
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to reproduce a long extract by A.M. Turing. The Indian Statistical Institute, through the editor of Sankhy¯a, kindly gave permission to quote A.N. Kolmogorov. We gratefully acknowledge the financial support by NSF Grant DCR8606366, ONR Grant N0001485k0445, ARO Grant DAAL0386K0171, the Natural Sciences
Kolmogorov complexity and the Recursion Theorem
, 2005
"... Several classes of diagonally nonrecursive (DNR) functions are characterized in terms of Kolmogorov complexity. In particular, a set of natural numbers A can wttcompute a DNR function iff there is a nontrivial recursive lower bound on the Kolmogorov complexity of the initial segments of A. Furth ..."
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Cited by 54 (16 self)
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Several classes of diagonally nonrecursive (DNR) functions are characterized in terms of Kolmogorov complexity. In particular, a set of natural numbers A can wttcompute a DNR function iff there is a nontrivial recursive lower bound on the Kolmogorov complexity of the initial segments of A
Kolmogorov Complexity in Randomness Extraction
"... We clarify the role of Kolmogorov complexity in the area of randomness extraction. We show that a computable function is an almost randomness extractor if and only if it is a Kolmogorov complexity extractor, thus establishing a fundamental equivalence between two forms of extraction studied in the l ..."
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We clarify the role of Kolmogorov complexity in the area of randomness extraction. We show that a computable function is an almost randomness extractor if and only if it is a Kolmogorov complexity extractor, thus establishing a fundamental equivalence between two forms of extraction studied
On strings with trivial Kolmogorov complexity
 INT J SOFTWARE INFORMATICS
, 2011
"... The Kolmogorov complexity of a string is the length of the shortest program that generates it. A binary string is said to have trivial Kolmogorov complexity if its complexity is at most the complexity of its length. Intuitively, such strings carry no more information than the information that is i ..."
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The Kolmogorov complexity of a string is the length of the shortest program that generates it. A binary string is said to have trivial Kolmogorov complexity if its complexity is at most the complexity of its length. Intuitively, such strings carry no more information than the information
Quantum Kolmogorov complexity
 J. Comput, System Sci
, 2001
"... In this paper we give a definition for quantum Kolmogorov complexity. In the classical setting, the Kolmogorov complexity of a string is the length of the shortest program that can produce this string as its output. It is a measure of the amount of innate randomness (or information) contained in the ..."
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In this paper we give a definition for quantum Kolmogorov complexity. In the classical setting, the Kolmogorov complexity of a string is the length of the shortest program that can produce this string as its output. It is a measure of the amount of innate randomness (or information) contained
The Kolmogorov complexity of infinite words
 7TH WORKSHOP ”DESCRIPTIONAL COMPLEXITY OF FORMAL SYSTEMS"
, 2007
"... We present a brief survey of results on relations between the Kolmogorov complexity of infinite strings and several measures of information content (dimensions) known from dimension theory, information theory or fractal geometry. Special emphasis is laid on bounds on the complexity of strings in con ..."
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We present a brief survey of results on relations between the Kolmogorov complexity of infinite strings and several measures of information content (dimensions) known from dimension theory, information theory or fractal geometry. Special emphasis is laid on bounds on the complexity of strings
Kolmogorov complexity as a language
, 1102
"... The notion of Kolmogorov complexity (=the minimal length of a program that generates some object) is often useful as a kind of language that allows us to reformulate some notions and therefore provide new intuition. In this survey we provide (with minimal comments) many different examples where noti ..."
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The notion of Kolmogorov complexity (=the minimal length of a program that generates some object) is often useful as a kind of language that allows us to reformulate some notions and therefore provide new intuition. In this survey we provide (with minimal comments) many different examples where
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