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Algebra i logika, 2018, Volume 57, Number 4, Pages 448–455
DOI: https://doi.org/10.17377/alglog.2018.57.403
(Mi al858)
 

This article is cited in 2 scientific papers (total in 2 papers)

Generic amplification of recursively enumerable sets

A. N. Rybalov

Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, ul. Pevtsova 13, Omsk, 644099 Russia
Full-text PDF (139 kB) Citations (2)
References:
Abstract: Generic amplification is a method that allows algebraically undecidable problems to generate problems undecidable for almost all inputs. It is proved that every simple negligible set is undecidable for almost all inputs, but it cannot be obtained via amplification from any undecidable set. On the other hand, it is shown that every recursively enumerable set with nonzero asymptotic density can be obtained via amplification from a set of natural numbers.
Keywords: algorithmically undecidable problem, generic amplification, undecidable set, simple negligible set, recursively enumerable set.
Funding agency Grant number
Russian Science Foundation 18-71-10028
Supported by Russian Science Foundation, project No. 18-71-10028.
Received: 19.04.2017
Revised: 15.04.2018
English version:
Algebra and Logic, 2018, Volume 57, Issue 4, Pages 289–294
DOI: https://doi.org/10.1007/s10469-018-9500-y
Bibliographic databases:
Document Type: Article
UDC: 510.5
Language: Russian
Citation: A. N. Rybalov, “Generic amplification of recursively enumerable sets”, Algebra Logika, 57:4 (2018), 448–455; Algebra and Logic, 57:4 (2018), 289–294
Citation in format AMSBIB
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\by A.~N.~Rybalov
\paper Generic amplification of recursively enumerable sets
\jour Algebra Logika
\yr 2018
\vol 57
\issue 4
\pages 448--455
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\jour Algebra and Logic
\yr 2018
\vol 57
\issue 4
\pages 289--294
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Linking options:
  • https://www.mathnet.ru/eng/al858
  • https://www.mathnet.ru/eng/al/v57/i4/p448
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и логика Algebra and Logic
    Statistics & downloads:
    Abstract page:198
    Full-text PDF :33
    References:35
    First page:1
     
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