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Minimization of Boolean functions
1965
Applications of Mathematics
Preserved Fulltext
INTRODUCTION For the minimization of combinational Boolean functions in a sum-of-product form, many methods have been developed. ...
J.\ Minimization of Boolean Functions. Bell System Technical Journal, 35,1956, pp. 1417-44. [4] Svoboda A.\ Some Applications of Contact Grids. Stroje na zpracovani informaci, VI, 1958, pp. 9-23. ...
l) Pointing out the essential terms of the minimal form of the function. ...
doi:10.21136/am.1965.102933
fatcat:dtql4rfe3fe5li6m4fis2qpny4
Symmetric Boolean Functions
2005
IEEE Transactions on Information Theory
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We present an extensive study of symmetric Boolean functions, especially of their cryptographic properties. ...
Our main result establishes the link between the periodicity of the simplified value vector of a symmetric Boolean function and its degree. ...
Boolean functions. ...
doi:10.1109/tit.2005.851743
fatcat:gm7vvfxzrrbbrj4mteagriz7jy
Irreducible Boolean Functions
[article]
2008
arXiv
pre-print
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Using a two-way correspondence between Boolean functions and hypergraphs, join-irreducibility translates into a combinatorial property of hypergraphs. ...
This paper is a contribution to the study of a quasi-order on the set Ω of Boolean functions, the simple minor quasi-order. We look at the join-irreducible members of the resulting poset Ω̃. ...
Describe the irreducible Boolean functions.
Boolean functions as polynomials. ...
arXiv:0801.2939v1
fatcat:ynp6l2yahjhkpkgeloakyuxocq
Reducible Boolean functions
1936
Bulletin of the American Mathematical Society
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as a Boolean function. ...
In this note I establish a condition that a Boolean function of n variables, say/, be reducible to a product of two Boolean functions f\ and / 2 , where ƒ involves variables not occurring in ft; and, similarly ...
If a Boolean function J\Xi, , X n ) be given, then a necessary and sufficient condition that there exist a g and an h, so that J\%ly ' ' ' y Xn) == g\%l) ' ' ' J %PJ VP ft\Xq, ' ' ' , X n ) j is that ...
doi:10.1090/s0002-9904-1936-06285-3
fatcat:s3mavsmxnzacbalrsksnnw3bra
Plotting Boolean Functions
1960
The American mathematical monthly
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PLOTTING BOOLEAN FUNCTIONS
WALTER E. ...
Consider the following Boolean function of four variables and six products in disjunctive normal form, where + denotes the Boolean sum, the immediate juxtaposition of elements designates the Boolean product ...
doi:10.2307/2308538
fatcat:rivrmne3jbgnxmlu5aje2bbjji
Boolean Random Functions
[chapter]
2014
Lecture notes in mathematics
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The Boolean RF are a generalization of the Boolean RACS. ...
Introduction This text reviews a family of random functions (RF) which is an extension of the binary Boolean model, and is of wide use for applications, the Boolean RF. ...
A Boolean islands RF Z(x) with intensity is built from this cylinder primary function. Give i) the univariate and bivariate distribution functions of Z(x). ...
doi:10.1007/978-3-319-10064-7_5
fatcat:kiwcdpk6gbfphmpyw6jxuwwzqi
Normal Boolean functions
2004
Journal of Complexity
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introduced the normality of bent functions. His work strengthened the interest for the study of the restrictions of Boolean functions on kdimensional flats providing the concept of k-normality. ...
Using recent results on the decomposition of any Boolean functions with respect to some subspace, we present several formulations of k-normality. ...
A Boolean function of m variables is a function from F m 2 into F 2 ; and we denote by B m the set of all Boolean functions of m variables. ...
doi:10.1016/j.jco.2003.08.010
fatcat:hnvroexyujgvhcofgiu46oub5m
Landscape Boolean functions
2019
Advances in Mathematics of Communications
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In this paper we define a class of generalized Boolean functions defined on F n 2 with values in Zq (we consider q = 2 k , k ≥ 1, here), which we call landscape functions (whose class contains generalized ...
In particular, we show that the previously published characterizations of generalized plateaued Boolean functions (which includes generalized bent and semibent) are in fact particular cases of this more ...
Certainly, every classical Boolean function is a landscape function. ...
doi:10.3934/amc.2019038
fatcat:xsfhvy4etzhyxlsbks7syk2nca
Landscape Boolean Functions
[article]
2018
arXiv
pre-print
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In this paper we define a class of Boolean and generalized Boolean functions defined on F_2^n with values in Z_q (mostly, we consider q=2^k), which we call landscape functions (whose class containing generalized ...
In particular, we show that the previously published characterizations of generalized bent and plateaued Boolean functions are in fact particular cases of this more general setting. ...
Given a generalized Boolean function f : F n 2 → Z q , the derivative D a f of f with respect to a vector a is the generalized Boolean function D a f : F n 2 → Z q defined by D a f (x) = f (x) − f (x ⊕ ...
arXiv:1806.05878v1
fatcat:c4qbba3xy5csrljffbzqcupdua
Quantum boolean functions
[article]
2010
arXiv
pre-print
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Fourier coefficients of boolean functions; and two quantum versions of a theorem of Friedgut, Kalai and Naor on the Fourier spectra of boolean functions. ...
In this paper we introduce the study of quantum boolean functions, which are unitary operators f whose square is the identity: f^2 = I. ...
boolean function. ...
arXiv:0810.2435v5
fatcat:suipqescfvhilnqvpy3n44dszy
Locally monotone Boolean and pseudo-Boolean functions
2012
Discrete Applied Mathematics
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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 ...
As it turns out, this parameterized notion provides a hierarchy of monotonicities for pseudo-Boolean (Boolean) functions. ...
We are interested in the so-called Boolean functions f : B n → B and pseudo-Boolean functions f : B n → R, where n denotes the arity of f . ...
doi:10.1016/j.dam.2012.03.006
fatcat:s63ju67nvfa7tlzbz2bdm7ou4i
The Stochastic Boolean Function Evaluation Problem for Symmetric Boolean Functions
[article]
2021
arXiv
pre-print
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We give two approximation algorithms solving the Stochastic Boolean Function Evaluation (SBFE) problem for symmetric Boolean functions. ...
As part of the design of the first algorithm, we prove that the goal value of any symmetric Boolean function is less than n(n+1)/2. ...
We thank Zach Pomerantz for experiments that gave us useful insights into the goal value of symmetric functions and the anonymous referees for their comments. ...
arXiv:2111.08793v2
fatcat:7fmb6nkx6bcf3mg5h2nyq3e7su
Almost Boolean Functions: The Design of Boolean Functions by Spectral Inversion
2004
Computational intelligence
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The design of Boolean functions with properties of cryptographic significance is a hard task. In this paper, we adopt an unorthodox approach to the design of such functions. ...
Our search space is the set of functions that possess the required properties. It is 'Booleanness' that is evolved. ...
Linear Boolean Function. ...
doi:10.1111/j.0824-7935.2004.00245.x
fatcat:rdlh433rgbe4nonrwy2ltrmj6m
Encoding Nested Boolean Functions as Quantified Boolean Formulas
2012
Journal on Satisfiability, Boolean Modeling and Computation
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We obtain an equivalence-preserving transformation in linear time from the PSPACEcomplete language of nested Boolean functions (NBF), also called Boolean programs, to prenex QBF. ...
In this paper, we consider the problem of compactly representing nested instantiations of propositional subformulas with different arguments as quantified Boolean formulas (QBF). ...
Definition 1 . 1 (Nested Boolean Function) A nested Boolean function (NBF) is a finite sequence D(f k ) = (f 0 , ..., f k ) of Boolean functions. ...
doi:10.3233/sat190092
fatcat:tnkmwi6gpndybbna42wix2fyyy
Learning Boolean Functions Incrementally
[chapter]
2012
Lecture Notes in Computer Science
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Classical learning algorithms for Boolean functions assume that unknown targets are Boolean functions over fixed variables. ...
Based on a classical learning algorithm for Boolean functions, we develop two learning algorithms to infer Boolean functions over enlarging sets of ordered variables. ...
Let f be a Boolean function over x n . ...
doi:10.1007/978-3-642-31424-7_10
fatcat:jwkaupohirgg7gwz5rbdffamau
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