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Implementation of Boolean functions with a bounded number of zeros by disjunctive normal forms

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Abstract

The problem of constructing simple disjunctive normal forms (DNFs) of Boolean functions with a small number of zeros is considered. The problem is of interest in the complexity analysis of Boolean functions and in its applications to data analysis. The method used is a further development of the reduction approach to the construction of DNFs of Boolean functions. A key idea of the reduction method is that a Boolean function is represented as a disjunction of Boolean functions with fewer zeros. In a number of practically important cases, this technique makes it possible to considerably reduce the complexity of DNF implementations of Boolean functions.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia

    Yu. V. Maximov

  2. National Research University “Higher School of Economics,”, Pokrovskii bulv. 11, Moscow, 109028, Russia

    Yu. V. Maximov

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  1. Yu. V. Maximov
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Correspondence to Yu. V. Maximov.

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Original Russian Text © Yu.V. Maximov, 2013, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2013, Vol. 53, No. 9, pp. 1569–1588.

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Maximov, Y.V. Implementation of Boolean functions with a bounded number of zeros by disjunctive normal forms. Comput. Math. and Math. Phys. 53, 1391–1409 (2013). https://doi.org/10.1134/S096554251309008X

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  • DOI: https://doi.org/10.1134/S096554251309008X

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