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Quantum algorithms for testing Boolean functions [PDF]
Electronic Proceedings in Theoretical Computer Science, 2010 We discuss quantum algorithms, based on the Bernstein-Vazirani algorithm, for finding which variables a Boolean function depends on. There are 2^n possible linear Boolean functions of n variables; given a linear Boolean function, the Bernstein-Vazirani ...
Erika Andersson +2 more
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Landscape Boolean Functions [PDF]
Advances in Mathematics of Communications, 2018 In this paper we define a class of Boolean and generalized Boolean functions defined on $\mathbb{F}_2^n$ with values in $\mathbb{Z}_q$ (mostly, we consider $q=2^k$), which we call landscape functions (whose class containing generalized bent, semibent ...
Riera, Constanza, Stanica, Pantelimon
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Join-irreducible Boolean functions [PDF]
Order, 2009 This paper is a contribution to the study of a quasi-order on the set $\Omega$ of Boolean functions, the \emph{simple minor} quasi-order. We look at the join-irreducible members of the resulting poset $\tilde{\Omega}$.
Bouaziz, Moncef +2 more
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Sensitivities and block sensitivities of elementary symmetric Boolean functions
Journal of Mathematical Cryptology, 2021 Boolean functions have important applications in molecular regulatory networks, engineering, cryptography, information technology, and computer science. Symmetric Boolean functions have received a lot of attention in several decades.
Zhang Jing, Li Yuan, Adeyeye John O.
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Further constructions of bent functions and their duals
IET Information Security, 2021 In 2012, Carlet et al. developed two secondary constructions of bent functions (Advances in Mathematics of Communications, 6: 305‐314) and proposed some applications for their constructions.
Yanjun Li +4 more
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Nonlinearity of incomplete Boolean functions: prioritizing spectra calculation [PDF]
Archives of Control Sciences, 2022 In this paper, a class of linear Boolean functions is analyzed. The Boolean function can be represented as disjoint cubes or in the form of a truth vector.
Piotr Porwik
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The Stochastic Boolean Function Evaluation problem for symmetric Boolean functions [PDF]
Discrete Applied Mathematics, 2022 Preliminary versions of these results appeared on Arxiv in arXiv:1806.10660. That paper contains results for both arbitrary costs and unit costs. This paper considers only arbitrary costs.
Dimitrios Gkenosis +3 more
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Testing Boolean Functions Properties [PDF]
Fundamenta Informaticae, 2021 The goal in the area of functions property testing is to determine whether a given black-box Boolean function has a particular given property or is ɛ-far from having that property. We investigate here several types of properties testing for Boolean functions (identity, correlations and balancedness) using the Deutsch-Jozsa algorithm (for the Deutsch ...
Zhengwei, Xie +4 more
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On Resilient Boolean and Vectorial Boolean Functions with High Nonlinearity
Mathematics, 2022 Boolean functions and vectorial Boolean functions are the most important nonlinear components of stream ciphers. They should satisfy several criteria such as high nonlinearity, proper resiliency and so on to guarantee the security of the whole system ...
Luyang Li +3 more
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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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