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JOURNALS // Diskretnaya Matematika // Archive

Diskr. Mat., 2021 Volume 33, Issue 1, Pages 91–102 (Mi dm1634)

This article is cited in 3 papers

Properties of proper families of Boolean functions

K. D. Tsaregorodtsev

Lomonosov Moscow State University

Abstract: We show that triangular families of Boolean functions comprise an exponentially small fraction of proper families of a given order. We prove that if $F$ is a proper family of Boolean functions, then the number of solutions of an equation $F(x) = A$ is even. Finally, we describe a new class of proper families of Boolean functions.

Keywords: proper family of Boolean functions, triangular family.

UDC: 519.716.322

Received: 01.02.2021

DOI: 10.4213/dm1634


 English version:
Discrete Mathematics and Applications, 2022, 32:5, 369–378


© Steklov Math. Inst. of RAS, 2025