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Minimization of Boolean functions

1965
*
Applications of Mathematics
*

INTRODUCTION For the minimization of combinational

doi:10.21136/am.1965.102933
fatcat:dtql4rfe3fe5li6m4fis2qpny4
*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*. ...##
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Symmetric Boolean Functions

2005
*
IEEE Transactions on Information Theory
*

We present an extensive study of symmetric

doi:10.1109/tit.2005.851743
fatcat:gm7vvfxzrrbbrj4mteagriz7jy
*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*. ...##
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Irreducible Boolean Functions
[article]

2008
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arXiv
*
pre-print

Using a two-way correspondence between

arXiv:0801.2939v1
fatcat:ynp6l2yahjhkpkgeloakyuxocq
*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. ...##
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Reducible Boolean functions

1936
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Bulletin of the American Mathematical Society
*

as a

doi:10.1090/s0002-9904-1936-06285-3
fatcat:s3mavsmxnzacbalrsksnnw3bra
*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 ...##
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Plotting Boolean Functions

1960
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The American mathematical monthly
*

PLOTTING

doi:10.2307/2308538
fatcat:rivrmne3jbgnxmlu5aje2bbjji
*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 ...##
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Boolean Random Functions
[chapter]

2014
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Lecture notes in mathematics
*

The

doi:10.1007/978-3-319-10064-7_5
fatcat:kiwcdpk6gbfphmpyw6jxuwwzqi
*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). ...##
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Normal Boolean functions

2004
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Journal of Complexity
*

introduced the normality of bent

doi:10.1016/j.jco.2003.08.010
fatcat:hnvroexyujgvhcofgiu46oub5m
*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. ...##
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Landscape Boolean functions

2019
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Advances in Mathematics of Communications
*

In this paper we define a class of generalized

doi:10.3934/amc.2019038
fatcat:xsfhvy4etzhyxlsbks7syk2nca
*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*. ...##
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Landscape Boolean Functions
[article]

2018
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arXiv
*
pre-print

In this paper we define a class of

arXiv:1806.05878v1
fatcat:c4qbba3xy5csrljffbzqcupdua
*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 ⊕ ...##
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Quantum boolean functions
[article]

2010
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arXiv
*
pre-print

Fourier coefficients of

arXiv:0810.2435v5
fatcat:suipqescfvhilnqvpy3n44dszy
*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*. ...##
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Locally monotone Boolean and pseudo-Boolean functions

2012
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Discrete Applied Mathematics
*

We propose local versions of monotonicity for

doi:10.1016/j.dam.2012.03.006
fatcat:s63ju67nvfa7tlzbz2bdm7ou4i
*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 . ...##
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The Stochastic Boolean Function Evaluation Problem for Symmetric Boolean Functions
[article]

2021
*
arXiv
*
pre-print

We give two approximation algorithms solving the Stochastic

arXiv:2111.08793v2
fatcat:7fmb6nkx6bcf3mg5h2nyq3e7su
*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. ...##
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Almost Boolean Functions: The Design of Boolean Functions by Spectral Inversion

2004
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Computational intelligence
*

The design of

doi:10.1111/j.0824-7935.2004.00245.x
fatcat:rdlh433rgbe4nonrwy2ltrmj6m
*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*. ...##
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Encoding Nested Boolean Functions as Quantified Boolean Formulas

2012
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Journal on Satisfiability, Boolean Modeling and Computation
*

We obtain an equivalence-preserving transformation in linear time from the PSPACEcomplete language of nested

doi:10.3233/sat190092
fatcat:tnkmwi6gpndybbna42wix2fyyy
*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*. ...##
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Learning Boolean Functions Incrementally
[chapter]

2012
*
Lecture Notes in Computer Science
*

Classical learning algorithms for

doi:10.1007/978-3-642-31424-7_10
fatcat:jwkaupohirgg7gwz5rbdffamau
*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 . ...
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