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Algebra i logika, 2016, Volume 55, Number 5, Pages 587–596
DOI: https://doi.org/10.17377/alglog.2016.55.505
(Mi al763)
 

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

A generic relation on recursively enumerable sets

A. N. Rybalovab

a Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, ul. Pevtsova 13, Omsk, 644099 Russia
b Omsk State Technical University, pr. Mira 11, Omsk, 644050 Russia
Full-text PDF (138 kB) Citations (2)
References:
Abstract: We introduce the concept of a generic relation for algorithmic problems, which preserves the property of being decidable for a problem for almost all inputs and possesses the transitive property. As distinct from the classical $m$-reducibility relation, the generic relation under consideration does not possess the reflexive property: we construct an example of a recursively enumerable set that is generically incomparable with itself. We also give an example of a set that is complete with respect to the generic relation in the class of recursively enumerable sets.
Keywords: generic relation, complete set, recursively enumerable set.
Funding agency Grant number
Russian Science Foundation 14-11-00085
Supported by Russian Science Foundation, project 14-11-00085.
Received: 13.04.2016
English version:
Algebra and Logic, 2016, Volume 55, Issue 5, Pages 387–393
DOI: https://doi.org/10.1007/s10469-016-9410-9
Bibliographic databases:
Document Type: Article
UDC: 510.5
Language: Russian
Citation: A. N. Rybalov, “A generic relation on recursively enumerable sets”, Algebra Logika, 55:5 (2016), 587–596; Algebra and Logic, 55:5 (2016), 387–393
Citation in format AMSBIB
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\by A.~N.~Rybalov
\paper A~generic relation on recursively enumerable sets
\jour Algebra Logika
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\vol 55
\issue 5
\pages 587--596
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\jour Algebra and Logic
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\vol 55
\issue 5
\pages 387--393
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  • https://www.mathnet.ru/eng/al/v55/i5/p587
  • 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
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    Abstract page:194
    Full-text PDF :30
    References:39
    First page:11
     
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