Results 1  10
of
371,099
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 ..."
Abstract

Cited by 2106 (119 self)
 Add to MetaCart
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
Improving the SpaceBounded Version of Muchnik’s Conditional Complexity Theorem via
, 1009
"... Abstract. Many theorems about Kolmogorov complexity rely on existence of combinatorial objects with specific properties. Usually the probabilistic method gives such objects with better parameters than explicit constructions do. But the probabilistic method does not give “effective” variants of such ..."
Abstract
 Add to MetaCart
of such theorems, i.e. variants for resourcebounded Kolmogorov complexity. We show that a “naive derandomization ” approach of replacing these objects by the output of NisanWigderson pseudorandom generator may give polynomialspace variants of such theorems. Specifically,weimprovetheprecedingpolynomialspace
NLprintable sets and Nondeterministic Kolmogorov Complexity
, 2003
"... This paper introduces nondeterministic spacebounded Kolmogorov complexity, and we show that it has some nice properties not shared by some other resourcebounded notions of Kcomplexity. ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
This paper introduces nondeterministic spacebounded Kolmogorov complexity, and we show that it has some nice properties not shared by some other resourcebounded notions of Kcomplexity.
Extracting Kolmogorov complexity with applications to dimension zeroone laws
 IN PROCEEDINGS OF THE 33RD INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES, AND PROGRAMMING
, 2006
"... We apply recent results on extracting randomness from independent sources to "extract " Kolmogorov complexity. For any ff; ffl? 0, given a string x with K(x) ? ffjxj, we show how to use a constant number of advice bits to efficiently compute another string y, jyj = \Omega (jxj), ..."
Abstract

Cited by 18 (2 self)
 Add to MetaCart
), with K(y) ? (1 \Gamma ffl)jyj. This result holds for both classical and spacebounded Kolmogorov complexity. We use the extraction procedure for spacebounded complexity to establish zeroone laws for polynomialspace strong dimension. Our results include: (i) If Dimpspace(E) ? 0, then Dimpspace(E=O(1
The Google similarity distance
, 2005
"... Words and phrases acquire meaning from the way they are used in society, from their relative semantics to other words and phrases. For computers the equivalent of ‘society ’ is ‘database, ’ and the equivalent of ‘use ’ is ‘way to search the database. ’ We present a new theory of similarity between ..."
Abstract

Cited by 316 (9 self)
 Add to MetaCart
words and phrases based on information distance and Kolmogorov complexity. To fix thoughts we use the worldwideweb as database, and Google as search engine. The method is also applicable to other search engines and databases. This theory is then applied to construct a method to automatically extract
Alternative notions of approximation and spacebounded computations
, 2003
"... We investigate alternative notions of approximation for problems inside P (deterministic polynomial time), and show that even a slightly nontrivial information about a problem may be as hard to obtain as the solution itself. For example, we prove that if one could eliminate even a single possibilit ..."
Abstract
 Add to MetaCart
and rank as to compute them exactly. Finally, we show that (in some precise sense) randomness can be nontrivially substituted for nondeterminism in space. Although it is believed that randomness does not give more than a constant factor advantage in space over determinism, it is not even known whether
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 ..."
Abstract
 Add to MetaCart
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
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 ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
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
Results 1  10
of
371,099