Related papers: Space-Bounded Kolmogorov Extractors
Randomness extraction is the process of constructing a source of randomness of high quality from one or several sources of randomness of lower quality. The problem can be modeled using probability distributions and min-entropy to measure…
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…
Algorithmic statistics studies explanations of observed data that are good in the algorithmic sense: an explanation should be simple i.e. should have small Kolmogorov complexity and capture all the algorithmically discoverable regularities…
A *dimension extractor* is an algorithm designed to increase the effective dimension -- i.e., the amount of computational randomness -- of an infinite binary sequence, in order to turn a "partially random" sequence into a "more random"…
Muchnik's theorem about simple conditional descriprion states that for all words $a$ and $b$ there exists a short program $p$ transforming $a$ to $b$ that has the least possible length and is simple conditional on $b$. This paper presents a…
Blasiok (SODA'18) recently introduced the notion of a subgaussian sampler, defined as an averaging sampler for approximating the mean of functions $f:\{0,1\}^m \to \mathbb{R}$ such that $f(U_m)$ has subgaussian tails, and asked for explicit…
The Boltzmann model for the random generation of "decomposable" combinatorial structures is a set of techniques that allows for efficient random sampling algorithms for a large class of families of discrete objects. The usual requirement of…
Trevisan has shown that constructions of pseudo-random generators from hard functions (the Nisan-Wigderson approach) also produce extractors. We show that constructions of pseudo-random generators from one-way permutations (the…
Kolmogorov complexity is often used as a convenient language for counting and/or probabilistic existence proofs. However, there are some applications where Kolmogorov complexity is used in a more subtle way. We provide one (somehow)…
Every topological space has a Kolmogorov quotient that is obtained by identifying topologically indistinguishable points, that is, points that are contained in exactly the same open sets. In this survey, we look at the relationship between…
The coding theorem for Kolmogorov complexity states that any string sampled from a computable distribution has a description length close to its information content. A coding theorem for resource-bounded Kolmogorov complexity is the key to…
This paper defines a new notion of bounded computable randomness for certain classes of sub-computable functions which lack a universal machine. In particular, we define such versions of randomness for primitive recursive functions and for…
We survey the Kolmogorov's approach to the notion of randomness through the Kolmogorov complexity theory. The original motivation of Kolmogorov was to give up a quantitative definition of information. In this theory, an object is randomness…
We discuss an acceptance-rejection algorithm for the random number generation from the Kolmogorov distribution. Since the cumulative distribution function (CDF) is expressed as a series, in order to obtain the density function we need to…
The paper studies randomness extraction from sources with bounded independence and the issue of independence amplification of sources, using the framework of Kolmogorov complexity. The dependency of strings $x$ and $y$ is ${\rm dep}(x,y) =…
Randomness extraction involves the processing of purely classical information and is therefore usually studied in the framework of classical probability theory. However, such a classical treatment is generally too restrictive for…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
We provide another proof to the EL Theorem. We show the tradeoff between compressibility of codebooks and their communication capacity. A resource bounded version of the EL Theorem is proven. This is used to prove three instances of…
Informally, an extractor delivers perfect randomness from a source that may be far away from the uniform distribution, yet contains some randomness. This task is a crucial ingredient of any attempt to produce perfectly random…
The information in an individual finite object (like a binary string) is commonly measured by its Kolmogorov complexity. One can divide that information into two parts: the information accounting for the useful regularity present in the…