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Shadow Minimization Boolean Function Reconstruction
Volume 35, Issue 1 (2024), pp. 1–20
Pub. online: 14 February 2024      Type: Research Article      Open accessOpen Access
Received
1 November 2023
Accepted
1 February 2024
Published
14 February 2024

Abstract

A special class of monotone Boolean functions coming from shadow minimization theory of finite set-systems – KK-MBF functions – is considered. These functions are a descriptive model for systems of compatible groups of constraints, however, the class of all functions is unambiguously complex and it is sensible to study relatively simple subclasses of functions such as KK-MBF. Zeros of KK-MBF functions correspond to initial segments of lexicographic order on hypercube layers. This property is used to simplify the recognition. Lexicographic order applies priorities over constraints which is applicable property of practices. Query-based algorithms for KK-MBF functions are investigated in terms of their complexities.

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Biographies

Aslanyan Levon
https://orcid.org/0000-0002-5354-2730
lasl@sci.am

L. Aslanyan graduated from Novosibirsk State University in 1968. He received his PhD in 1976, and his doctorate in 1997. He is a professor since 1997 and a corresponding member of National Academy of Sciences of the Republic of Armenia since 2014. He currently heads the Department of Discrete Modelling, Analysis, and Recognition at the Institute for Informatics and Automation Problems of the NAS RA. Research interests: mathematical logic, discrete mathematics, mathematical theory of pattern recognition and artificial intelligence.

Katona Gyula
https://orcid.org/0000-0002-0188-0391
katona.gyula.oh@renyi.hu

G. Katona, prof., is a doctor of the mathematical sciences. He is an academician of the Hungarian Academy of Sciences, a member of the European Academy of Sciences, a foreign member of the Bulgarian Academy of Sciences, a research professor at Alfred Renyi Institute of Mathematics, Hungarian Academy of Sciences, and a professor at the Eötvös L. University. His main research areas include extreme combinatorial aanalysis.

Sahakyan Hasmik
https://orcid.org/0000-0002-8449-6845
hsahakyan@sci.am

H. Sahakyan graduated from Yerevan State University. She received her PhD in 2002 and her doctorate in 2018. She is currently a scientific secretary of the Institute for Informatics and Automation Problems of the NAS RA and a leading researcher at the Discrete Mathematics Department. Scientific interests: combinatorics, discrete optimization, discrete tomography, artificial intelligence, and data mining.


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Keywords
monotone Boolean function reconstruction lexicographic order shadow KK-MBF class

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