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06111 Executive Summary – Complexity of Boolean Functions [PDF]
, 2006 We briefly describe the state of the art concerning the complexity of discrete functions. Computational models and analytical techniques are summarized. After describing the formal organization of the Dagstuhl seminar "Complexity of Boolean Functions"
van Melkebeek, Dieter +3 more
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Affine equivalence of monomial rotation symmetric Boolean functions: A Pólya’s theorem approach
Journal of Mathematical Cryptology, 2016 Two Boolean functions are affine equivalent if one can be obtained from the other by applying an affine transformation to the input variables. For a long time, there have been efforts to investigate the affine equivalence of Boolean functions. Due to the
Cusick Thomas W. +2 more
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Discovering Non-Linear Boolean Functions by Evolving Walsh Transforms with Genetic Programming
Algorithms, 2023 Stream ciphers usually rely on highly secure Boolean functions to ensure safe communication within unsafe channels. However, discovering secure Boolean functions is a non-trivial optimization problem that has been addressed by many optimization ...
Luigi Rovito +2 more
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06111 Abstracts Collection – Complexity of Boolean Functions [PDF]
, 2006 From 12.03.06 to 17.03.06, the Dagstuhl Seminar 06111 ``Complexity of Boolean Functions'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research,
van Melkebeek, Dieter +3 more
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Evolving sensitivity balances Boolean networks [PDF]
, 2012 We investigate the sensitivity of Boolean Networks (BNs) to mutations. We are interested in Boolean Networks as a model of Gene Regulatory Networks (GRNs). We adopt Ribeiro and Kauffman’s Ergodic Set and use it to study the long term dynamics of a BN. We
Turner, Matthew S. +9 more
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On the Power of Choice for Boolean Functions
SIAM Journal on Discrete Mathematics, 2022 In this paper we consider a variant of the well-known Achlioptas process for graphs adapted to monotone Boolean functions. Fix a number of choices $r\in \mathbb N$ and a sequence of increasing functions $(f_n)_{n\ge 1}$ such that, for every $n\ge 1$, $f_n:\{0,1\}^n\mapsto \{0,1\}$.
Nicolas Fraiman +2 more
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Analyzing capacitated networks via Boolean-based coherent pseudo-Boolean functions [PDF]
Network Biology, 2021 This paper introduces a novel method for analyzing capacitated networks through the utilization of the concept of a "probability-ready expression" for a Boolean-based coherent pseudo-Boolean function. Our main concern is to assess the performance indexes
Ali Muhammad Ali Rushdi +1 more
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On connected Boolean functions
Discrete Applied Mathematics, 1999 Various classes of Boolean functions are introduced: connected, strongly connected, geodetic, convex, strongly convex and concordant. They are characterized by some properties of the subgraph of the Boolean hypercube induced by the (false) true points of a function.
Ekin, O., Hammer, P. L., Kogan, A.
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Quantum algorithms for testing and learning Boolean functions
, 2013 We discuss quantum algorithms based on the Bernstein-Vazirani algorithm for finding which input variables a Boolean function depends on. There are 2(n) possible linear Boolean functions of n input variables; given a linear Boolean function, the Bernstein-
Floess, Dominik +2 more
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Constructing optimized Boolean functions
Tongxin xuebao, 2006 Considering connections of characteristics,aiming construction for the optimized Boolean functions,new method based on Bent function,discrete Walsh spectrum and characteristics matrices were presented by concatenating,breaking,and revising output ...
CHEN Wei1, YANG Yi-xian1, NIU Xin-xin2
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