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Joint Realizability of Monotone Boolean Functions. [PDF]
Theor Comput Sci, 2022 36 pages, 9 ...
Crawford-Kahrl P, Cummins B, Gedeon T.
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Locally monotone Boolean and pseudo-Boolean functions [PDF]
Discrete Applied Mathematics, 2012 We propose local versions of monotonicity for Boolean and pseudo-Boolean functions: say that a pseudo-Boolean (Boolean) function is p-locally monotone if none of its partial derivatives changes in sign on tuples which differ in less than p positions. As it turns out, this parameterized notion provides a hierarchy of monotonicities for pseudo-Boolean ...
Miguel Couceiro +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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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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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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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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Multi-Angle Fast Neural Tangent Kernel Classifier
Applied Sciences, 2022 Multi-kernel learning methods are essential kernel learning methods. Still, the base kernel functions in most multi-kernel learning methods only with select kernel functions with shallow structures, which are weak for large-scale uneven data.
Yuejing Zhai, Zhouzheng Li, Haizhong Liu
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On the Lyapunov Exponent of Monotone Boolean Networks †
Mathematics, 2020 Boolean networks are discrete dynamical systems comprised of coupled Boolean functions. An important parameter that characterizes such systems is the Lyapunov exponent, which measures the state stability of the system to small perturbations.
Ilya Shmulevich
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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.
Eleonora Testa +4 more
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