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Prikl. Diskr. Mat., 2017, Number 36, Pages 106–112 (Mi pdm582)  

This article is cited in 3 scientific papers (total in 3 papers)

Mathematical Foundations of Informatics and Programming

On generic NP-completeness of the Boolean satisfiability problem

A. N. Rybalov

Omsk State Technical University, Omsk, Russia

Abstract: Generic-case approach to algorithmic problems was suggested by Miasnikov, Kapovich, Schupp and Shpilrain in 2003. This approach studies behavior of an algorithm on typical (almost all) inputs and ignores the rest of inputs. Many classical undecidable or hard algorithmic problems become feasible in the generic case. But there are generically hard problems. In this paper we introduce a notion of generic polynomial reducibility algorithmic problems, which preserve the property of polynomial decidability of the problem for almost all inputs and has the property of transitivity. It is proved that the classical satisfiability problem of Boolean formulas is complete with respect to this generic reducibility in the generic analogue of class NP.

Keywords: generic complexity, Boolean satisfiability problem, NP-completeness.

Funding Agency Grant Number
Russian Science Foundation 17-11-01117


DOI: https://doi.org/10.17223/20710410/36/8

Full text: PDF file (651 kB)
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Bibliographic databases:

UDC: 510.52

Citation: A. N. Rybalov, “On generic NP-completeness of the Boolean satisfiability problem”, Prikl. Diskr. Mat., 2017, no. 36, 106–112

Citation in format AMSBIB
\Bibitem{Ryb17}
\by A.~N.~Rybalov
\paper On generic NP-completeness of the Boolean satisfiability problem
\jour Prikl. Diskr. Mat.
\yr 2017
\issue 36
\pages 106--112
\mathnet{http://mi.mathnet.ru/pdm582}
\crossref{https://doi.org/10.17223/20710410/36/8}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Rybalov, “Generic NP-incomplete problems”, Mechanical Science and Technology Update (MSTU-2018), Journal of Physics Conference Series, 1050, IOP Publishing Ltd, 2018, 012072  crossref  isi  scopus
    2. A. V. Seliverstov, “O dvoichnykh resheniyakh sistem uravnenii”, PDM, 2019, no. 45, 26–32  mathnet  crossref
    3. A. N. Rybalov, “O genericheskoi NP-polnote problemy vypolnimosti bulevykh skhem”, PDM, 2020, no. 47, 101–107  mathnet  crossref
  • Прикладная дискретная математика
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