On positive, linear and quadratic Boolean functions
Sergiu Rudeanu (2012)
Kragujevac Journal of Mathematics
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Sergiu Rudeanu (2012)
Kragujevac Journal of Mathematics
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Grzegorz Bancerek (2012)
Formalized Mathematics
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We introduce an algebra with free variables, an algebra with undefined values, a program algebra over a term algebra, an algebra with integers, and an algebra with arrays. Program algebra is defined as universal algebra with assignments. Programs depend on the set of generators with supporting variables and supporting terms which determine the value of free variables in the next state. The execution of a program is changing state according to successor function using supporting terms. ...
Antonio Aizpuru (1996)
Colloquium Mathematicae
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We study local interpolation properties and local supremum properties for a Boolean algebra. In particular, we present a new condition that is sufficient for the Nikodym property.
Čomić, Lidija, Tošić, Ratko (2004)
Novi Sad Journal of Mathematics
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Jörg Flum (1999)
Banach Center Publications
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Rasiowa and Sikorski [5] showed that in any Boolean algebra there is an ultrafilter preserving countably many given infima. In [3] we proved an extension of this fact and gave some applications. Here, besides further remarks, we present some of these results in a more general setting.
Grzegorz Bancerek (2013)
Formalized Mathematics
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We analyse three algorithms: exponentiation by squaring, calculation of maximum, and sorting by exchanging in terms of program algebra over an algebra.
Piotr Porwik (2004)
Control and Cybernetics
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Sergiu Rudeanu (1998)
Mathware and Soft Computing
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An abstract form of modus ponens in a Boolean algebra was suggested in [1]. In this paper we use the general theory of Boolean equations (see e.g. [2]) to obtain a further generalization. For a similar research on Boolean deduction theorems see [3].
Tošić, Ratko, Čomić, Lidija (2000)
Novi Sad Journal of Mathematics
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Huaning Liu, Min Zhang (2016)
Acta Arithmetica
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In a series of papers many Boolean functions with good cryptographic properties were constructed using number-theoretic methods. We construct a large family of Boolean functions by using polynomials over finite fields, and study their cryptographic properties: maximum Fourier coefficient, nonlinearity, average sensitivity, sparsity, collision and avalanche effect.
Steven Garavaglia, J. M. Plotkin (1984)
Colloquium Mathematicae
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Bouyuklieva, Stefka, Bouyukliev, Iliya (2016)
Serdica Journal of Computing
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In this article, we study two representations of a Boolean function which are very important in the context of cryptography. We describe Möbius and Walsh Transforms for Boolean functions in details and present effective algorithms for their implementation. We combine these algorithms with the Gray code to compute the linearity, nonlinearity and algebraic degree of a vectorial Boolean function. Such a detailed consideration will be very helpful for students studying the design of block...