# Space-Bounded Kolmogorov Extractors

@article{Musatov2012SpaceBoundedKE, title={Space-Bounded Kolmogorov Extractors}, author={Daniil Musatov}, journal={ArXiv}, year={2012}, volume={abs/1203.3674} }

An extractor is a function that receives some randomness and either “improves” it or produces “new” randomness. There are statistical and algorithmical specifications of this notion. We study an algorithmical one called Kolmogorov extractors and modify it to resource-bounded version of Kolmogorov complexity. Following Zimand we prove the existence of such objects with certain parameters. The utilized technique is “naive” derandomization: we replace random constructions employed by Zimand by…

## 4 Citations

### On Extracting Space-bounded Kolmogorov Complexity

- Computer Science, MathematicsTheory of Computing Systems
- 2014

It is proved that in space-bounded framework any string a has a “universal code” p such that two properties hold: first, p is simple conditional on a, and second, for any string b of polynomial length a issimple conditional on b and the Cs(a|b)-bit prefix of p, causing the term “extraction”.

### Improving the Space-Bounded Version of Muchnik’s Conditional Complexity Theorem via “Naive” Derandomization

- Computer Science, MathematicsTheory of Computing Systems
- 2012

It is shown that a “naive derandomization” approach of replacing these objects by the output of Nisan-Wigderson pseudo-random generator can give polynomial-space variants of such theorems, i.e. variants for resource-bounded Kolmogorov complexity.

### Kolmogorov Complexity and Algorithmic Randomness

- Computer Science
- 2017

The book under review presents a rich account of numerous earlier definitions of randomness, their interconnection with algorithmic complexity, and their applications and presents some concrete examples of the boundary between randomness and nonrandomness.

### Short lists with short programs in short time

- Mathematics, Computer Science2013 IEEE Conference on Computational Complexity
- 2013

It is shown that for some standard machines, computable functions generating lists with 0-short programs must have infinitely often list sizes proportional to 2|x|.

## References

SHOWING 1-10 OF 15 REFERENCES

### Kolmogorov Complexity in Randomness Extraction

- Mathematics, Computer ScienceTOCT
- 2011

It is shown 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 literature: Kolmogsorov extraction and randomness extraction.

### Improving the Space-Bounded Version of Muchnik’s Conditional Complexity Theorem via “Naive” Derandomization

- Computer Science, MathematicsTheory of Computing Systems
- 2012

It is shown that a “naive derandomization” approach of replacing these objects by the output of Nisan-Wigderson pseudo-random generator can give polynomial-space variants of such theorems, i.e. variants for resource-bounded Kolmogorov complexity.

### Possibilities and impossibilities in Kolmogorov complexity extraction

- Computer ScienceArXiv
- 2011

The connection between extractors and Kolmogorov extractors is presented and the basic positive and negative results concerning Kolmogsorov complexity extraction are presented.

### Two Sources Are Better than One for Increasing the Kolmogorov Complexity of Infinite Sequences

- Computer Science, MathematicsTheory of Computing Systems
- 2009

A uniform effective procedure having as input two independent sequences with positive but arbitrarily small constant randomness rate is displayed, and the transformation is a truth-table reduction and the output has randoms rate arbitrarily close to 1.

### Symmetry of Information and Bounds on Nonuniform Randomness Extraction via Kolmogorov Extractors

- Computer Science, Mathematics2011 IEEE 26th Annual Conference on Computational Complexity
- 2011

We prove a strong Symmetry of Information relation for random strings (in the sense of Kolmogorov complexity) and establish tight bounds on the amount on nonuniformity that is necessary for…

### An Introduction to Randomness Extractors

- MathematicsICALP
- 2011

The main concepts of this area of "randomness extraction" are surveyed: deterministic extractors, seeded extractors and multiple sources extractors.

### Extracting Kolmogorov complexity with applications to dimension zero-one laws

- Mathematics, Computer ScienceInf. Comput.
- 2005

### Impossibility of Independence Amplification in Kolmogorov Complexity Theory

- Mathematics, Computer ScienceMFCS
- 2010

It is shown that there exists a computable Kolmogorov extractor f such that, for any two n-bit strings with complexity s(n) and dependency α(n), it outputs a string of length s( n), conditioned by any one of the input strings.

### Extracting the Kolmogorov Complexity of Strings and Sequences from Sources with Limited Independence

- Mathematics, Computer ScienceSTACS
- 2009

It is shown that from any two strings with sufficiently large Kolmogorov complexity and sufficiently small dependence, one can effectively construct a string that is random even conditioned by any one of the input strings.