On the Algebraic Normal Form and Walsh Spectrum of Symmetric Functions over Finite Rings

2012 ◽  
pp. 92-107
Author(s):  
Boris Batteux
Keyword(s):  
Normal Form ◽  
Symmetric Functions ◽  
Finite Rings ◽  
Walsh Spectrum ◽  
Algebraic Normal Form

scholarly journals Certificate complexity and symmetry of nested canalizing functions

2021 ◽  
Vol vol. 23, no. 3 (Combinatorics) ◽  
Author(s):  
Yuan Li ◽  
Frank Ingram ◽  
Huaming Zhang
Keyword(s):  
Normal Form ◽  
Computer Science ◽  
General Formula ◽  
Boolean Functions ◽  
Regulatory Networks ◽  
Direct Proof ◽  
Interesting Property ◽  
Partial Symmetry ◽  
Algebraic Normal Form

Boolean nested canalizing functions (NCFs) have important applications in molecular regulatory networks, engineering and computer science. In this paper, we study their certificate complexity. For both Boolean values $b\in\{0,1\}$, we obtain a formula for $b$-certificate complexity and consequently, we develop a direct proof of the certificate complexity formula of an NCF. Symmetry is another interesting property of Boolean functions and we significantly simplify the proofs of some recent theorems about partial symmetry of NCFs. We also describe the algebraic normal form of $s$-symmetric NCFs. We obtain the general formula of the cardinality of the set of $n$-variable $s$-symmetric Boolean NCFs for $s=1,\dots,n$. In particular, we enumerate the strongly asymmetric Boolean NCFs.

Superpoly algebraic normal form monomial test on Trivium

2013 ◽  
Vol 7 (3) ◽  
pp. 230-238 ◽  
Author(s):  
Ali Vardasbi ◽  
Mahmoud Salmasizadeh ◽  
Javad Mohajeri
Keyword(s):  
Normal Form ◽  
Algebraic Normal Form

Computing Walsh coefficients from the algebraic normal form of a Boolean function

2014 ◽  
Vol 6 (4) ◽  
pp. 335-358 ◽  
Author(s):  
Xinxin Gong ◽  
Bin Zhang ◽  
Wenling Wu ◽  
Dengguo Feng
Keyword(s):  
Normal Form ◽  
Boolean Function ◽  
Algebraic Normal Form

Optimizations in computing the algebraic normal form transform of Boolean functions

2021 ◽  
Author(s):  
Maria Pashinska-Gadzheva ◽  
Valentin Bakoev ◽  
Iliya Bouyukliev ◽  
Dushan Bikov
Keyword(s):  
Normal Form ◽  
Boolean Functions ◽  
Algebraic Normal Form
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