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On maximal and minimal elements of partially ordered sets of Boolean degrees

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Abstract

The paper addresses the “weakest” algorithmic reducibility—Boolean reducibility. Under study are the partially ordered sets of Boolean degrees L Q corresponding to the various closed classes of Boolean functions Q. The set L Q is shown to have no maximal elements for many closed classes Q. Some examples are given of a sufficiently large classes Q for which L Q contains continuum many maximal elements. It is found that the sets of degrees corresponding to the closed classes T 01 and SM contain continuum many minimal elements.

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Authors and Affiliations

  1. LomonosovMoscow State University, Leninskie gory, Moscow, 119991, Russia

    S. S. Marchenkov

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  1. S. S. Marchenkov
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Correspondence to S. S. Marchenkov.

Additional information

Original Russian Text © S.S. Marchenkov, 2013, published in Diskretnyi Analiz i Issledovanie Operatsii, 2013, Vol. 20, No. 2, pp. 88–101.

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Marchenkov, S.S. On maximal and minimal elements of partially ordered sets of Boolean degrees. J. Appl. Ind. Math. 7, 549–556 (2013). https://doi.org/10.1134/S1990478913040091

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  • DOI: https://doi.org/10.1134/S1990478913040091

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