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Maximal faces of Boolean functions with a small number of zeroes

  • Mathematical Methods in Pattern Recognition
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Abstract

It is shown that there are no kernel faces in a contracted disjunctive normal form of a complete Boolean function (in seven or more variables) with a small number of zeroes. In addition, a lower bound for the number of faces that go through the same point is found.

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References

  1. Yu. I. Zhuravlev and A. Yu. Kogan, “Implementation of Boolean Functions with Small Number of Zeros by Disjunctive Normal Forms and Related Problems,” Dokl. Akad. Nauk USSR 285(4), 795–799 (1985).

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  2. Yu. I. Zhuravlev and A. Yu. Kogan, “Algorithm for Generating the Disjunctive Normal Form Equivalent to the Product of Left Parts of Nelson Type Equations,” Zh. Vychisl. Mat. Mat. Fiz. 26(8), 1243–1249 (1986).

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  3. A. Yu. Kogan, “On Disjunctive Normal Forms of Boolean Functions with Small Number of Zeros,” Zh. Vychisl. Mat. Mat. Fiz. 27(6), 924–931 (1987).

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Authors and Affiliations

  1. Dorodnicyn Computing Centre, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

    M. Yu. Romanov

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  1. M. Yu. Romanov
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Correspondence to M. Yu. Romanov.

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Mikhail Yur’evich Romanov. Born in 1982. Graduated from the Moscow Institute of Physics and Technology (MIPT) in 2005. In 2008 finished his post-graduate study at Dorodnicyn Computing Centre, Russian Academy of Sciences (CC RAS) and received candidate’s degree in physical and mathematical sciences. Currently project manager in the company Svyaznoi. Author of six articles. Scientific interests include problems on intelligent data analysis, problems on discrete optimization, and applied systems for recognition and prediction.

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Romanov, M.Y. Maximal faces of Boolean functions with a small number of zeroes. Pattern Recognit. Image Anal. 20, 474–478 (2010). https://doi.org/10.1134/S1054661810040073

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  • DOI: https://doi.org/10.1134/S1054661810040073

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