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A Generic m-Reducibility

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Sailing Routes in the World of Computation (CiE 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10936))

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Abstract

Kapovich, Myasnikov, Schupp and Shpilrain in 2003 developed generic approach to algorithmic problems, which considers an algorithmic problem on “most” of the inputs (i.e., on a generic set) instead of the entire domain and ignores it on the rest of inputs (a negligible set). Jockusch and Schupp in 2012 began the study of generic computability in the context of classical computability theory. In particular, they defined a generic analog of Turing reducibility. In this paper we introduce a generic analog of m-reducibility as m-reducibility by computable functions, which preserve the non-negligibility of sets. We study generic m-reducibility of computable and c.e. sets. We prove the existence of generically m-complete c.e. sets, incomparable c.e. sets and m-degrees, which contain more than one generic m-degree.

A. Rybalov—Supported by the program of basic scientific researches SB RAS II.1, project 0314-2016-0004.

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References

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Pevtsova 13, Omsk, 644099, Russia

    Alexander Rybalov

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  1. Alexander Rybalov
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Correspondence to Alexander Rybalov .

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Editors and Affiliations

  1. Kiel University, Kiel, Germany

    Florin Manea

  2. Queens College, CUNY, Queens, New York, USA

    Russell G. Miller

  3. Kiel University, Kiel, Germany

    Dirk Nowotka

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Rybalov, A. (2018). A Generic m-Reducibility. In: Manea, F., Miller, R., Nowotka, D. (eds) Sailing Routes in the World of Computation. CiE 2018. Lecture Notes in Computer Science(), vol 10936. Springer, Cham. https://doi.org/10.1007/978-3-319-94418-0_36

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  • DOI: https://doi.org/10.1007/978-3-319-94418-0_36

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94417-3

  • Online ISBN: 978-3-319-94418-0

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