Properties of proper families of Boolean functions
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Kirill D. Tsaregorodtsev
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.
Note
Originally published in Diskretnaya Matematika (2021) 33,№1, 91–102 (in Russian).
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Articles in the same Issue
- Contents
- Classification of Hadamard products of one-codimensional subcodes of Reed–Muller codes
- Asymptotical local probabilities of lower deviations for branching process in random environment with geometric distributions of descendants
- On the “tree” structure of natural numbers
- Estimates of lengths of shortest nonzero vectors in some lattices, II
- Curvature of the Boolean majority function
- Properties of proper families of Boolean functions
Articles in the same Issue
- Contents
- Classification of Hadamard products of one-codimensional subcodes of Reed–Muller codes
- Asymptotical local probabilities of lower deviations for branching process in random environment with geometric distributions of descendants
- On the “tree” structure of natural numbers
- Estimates of lengths of shortest nonzero vectors in some lattices, II
- Curvature of the Boolean majority function
- Properties of proper families of Boolean functions
