Results 1 to 10 of about 86 (78)
Cryptographic properties of monotone Boolean functions
Journal of Mathematical Cryptology, 2016 We prove various results on monotone Boolean functions. In particular, we prove a conjecture proposed recently, stating that there are no monotone bent Boolean functions.
Carlet Claude +3 more
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Joint realizability of monotone Boolean functions
Theoretical Computer Science, 2022 36 pages, 9 ...
Tomáš Gedeon +2 more
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Counting inequivalent monotone Boolean functions
Discrete Applied Mathematics, 2014 Monotone Boolean functions (MBFs) are Boolean functions $f: {0,1}^n \rightarrow {0,1}$ satisfying the monotonicity condition $x \leq y \Rightarrow f(x) \leq f(y)$ for any $x,y \in {0,1}^n$. The number of MBFs in n variables is known as the $n$th Dedekind number.
Tamon Stephen, Timothy Yusun
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Mapping Monotone Boolean Functions into Majority [PDF]
IEEE Transactions on Computers, 2019 We consider the problem of decomposing monotone Boolean functions into majority-of-three operations, with a particular focus on decomposing the majority-$n$n function. When targeting monotone Boolean functions, Shannon’s expansion can be expressed by a single majority-of-three operation.
Mathias Soeken +2 more
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On the Number of Inequivalent Monotone Boolean Functions of 9 Variables
IEEE Transactions on Information TheoryWe provide the first-ever calculation of the number of inequivalent monotone Boolean functions of 9 variables, which is equal to 789,204,635,842,035,040,527,740,846,300,252,680.
Bartłomiej Pawelski
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Conditional Dichotomy of Boolean Ordered Promise CSPs [PDF]
TheoretiCS, 2023 Promise Constraint Satisfaction Problems (PCSPs) are a generalization of Constraint Satisfaction Problems (CSPs) where each predicate has a strong and a weak form and given a CSP instance, the objective is to distinguish if the strong form can be ...
Joshua Brakensiek +2 more
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Application of Election Functions to Estimate the Number of Monotone Self-Dual Boolean functions
Моделирование и анализ информационных систем, 2022 One of the problems of modern discrete mathematics is R. Dedekind problem on the number of monotone boolean functions. For other precomplete classes, general formulas for the number of functions of the classes had been found, but it has not been found so
Leonid Y. Bystrov, Egor V. Kuzmin
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Approximating the distance to monotonicity of Boolean functions [PDF]
Random Structures & Algorithms, 2020 AbstractWe design a nonadaptive algorithm that, given oracle access to a function which is ‐far from monotone, makes poly queries and returns an estimate that, with high probability, is an ‐approximation to the distance of to monotonicity. The analysis of our algorithm relies on an improvement to the directed isoperimetric inequality of Khot, Minzer,
Ramesh Krishnan S. Pallavoor +2 more
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The Zhegalkin Polynomial of Multiseat Sole Sufficient Operator
Моделирование и анализ информационных систем, 2023 Among functionally complete sets of Boolean functions, sole sufficient operators are of particular interest. They have a wide range of applicability and are not limited to the two-seat case.
Leonid Y. Bystrov, Egor V. Kuzmin
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Monotone Boolean Functions with s Zeros Farthest from Threshold Functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Let $T_t$ denote the $t$-threshold function on the $n$-cube: $T_t(x) = 1$ if $|\{i : x_i=1\}| \geq t$, and $0$ otherwise. Define the distance between Boolean functions $g$ and $h$, $d(g,h)$, to be the number of points on which $g$ and $h$ disagree.
Kazuyuki Amano, Jun Tarui
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