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Approximate polynomial degree of Boolean functions and its - EECS
Abstract. The approximate polynomial degree of a Boolean function f : {0, 1}n → .... Another direct consequence of Theorem 2..3 states that if a function is highly ...

On the Complexity of Boolean Functions in Different Characteristics
Jun 6, 2009 ... The results above show a very basic relation between the degrees of Boolean functions over different characteristic. A natural question to ask is ...

Boolean Algebra
A Boolean function of degree n or of order n is a function with domain ... pairs a value from B. This means there are 24 = 16 different Boolean functions of order 2.

On Boolean functions with low sensitivity - Center for the Theory of
Sep 5, 2014 ... We review several complexity measures for Boolean functions ... function can be studied in many ways by considering different ... Fourier degree and approximate degree are polynomially related to decision tree complexity.

Algebraic Attacks and Decomposition of Boolean Functions - IACR
degree multiples of Boolean functions are a basic concern in the design of stream ciphers ... Boolean function has a low degree multiple is estimated. Keywords ...

Cryptographically Significant Boolean functions: Construction - IACR
In a different direction we identify that functions, having low degree ... Given a Boolean function f on n-variables, different kinds of scenarios related to low degree ...

The Complexity of Boolean Functions in Different Characteristics
May 12, 2010 ... º If f has degree o(log n) modulo p, then it must have degree Ω(n1−o(1)) modulo q . Thus a Boolean function has degree o(log n) in at most one ...

On the Degree of Polynomials that Approximate Symmetric Boolean
of approximate degree of symmetric boolean functions and provide a com- piete ( up to a constant factor) solution. .... another suitably chosen polynomial so. 469 ...

Restrictions of Nondegenerate Boolean Functions and Degree
on all the remaining n − 1 variables. We also consider lower bounds on the degrees of polynomials representing a Boolean function over different rings. Let dq(f).

Computing Boolean Functions: Exact Quantum Query Algorithms
computing the value of Boolean function and its relation to the degree of ..... Symmetry in final distribution of amplitudes for different inputs for algorithm A1.

approximate majority function , which is defined - Brown University
on a different level set, and arbitrary 0-1 values on other Boolean inputs. We show ... Our results instead bound the degree of a large class of Boolean functions.

Boolean Functions for Cryptography and Error Correcting - LAGA
These two different notations will be necessary because some .... we have: Proposition 2 The algebraic degree d◦f of any n-variable Boolean function f equals ...

On the Minimal Fourier Degree of Symmetric Boolean Functions - Sites
polynomial G(z) = F(z + 1) − F(z) was studied modulo different primes, however the ... on the degree of non-constant symmetric Boolean functions, when ...
updated manuscript.pdf

Boolean Functions and Boolean Maps
We don't yet know whether these functions are different (but we'll see it immediately) ... Definition The degree of a Boolean function f ∈ Fn as polynomial expres-.

Download - UCLA Computer Science
The threshold degree of a Boolean function f : {0, 1}n → {−1, +1} is the least degree ... theory is another area in which the threshold degree of Boolean functions.

Analysis of Boolean Functions
Feb 27, 2012 ... For example, the different representations of the parity function χS are given in Table 1. ... The F2 degree of a boolean function f : Fn. 2 → {−1,1} ...

Propagation Characteristics of Boolean Functions 1 Introduction
function of Boolean functions is used to study propagation characteristics of these ... rion are generalized in a Propagation Criterion of degree k. ... for individual output bits of S-boxes as well as for the relation between the different func-. tions.

On the nonlinearity of boolean functions - Institut de Mathématiques
properties of systems depend on the nonlinearity of a boolean function. ... Dillon [ 4]). For these, the degree of nonlinearity is well known, we know how to construct ... In the case where m is odd, the situation is quite different. We do not know the ...

The threshold order of a Boolean function - ScienceDirect
A Boolean function is said to be a threshold function of order m if the surface required to separate the true from the false vectors is a polynomial of degree m.

On the Symmetric Property of Homogeneous Boolean Functions
classes of degree 3 homogeneous boolean functions: the first class is de- .... all different boolean functions generated by permutations in Sn. Therefore, the set is  ...

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