A Duality Relationship Between Boolean Functions in CNF and DNF Derivable from the Same Training Examples

2010 ◽  
pp. 147-150
Author(s):  
Evangelos Triantaphyllou
Keyword(s):  
Boolean Functions ◽  
Training Examples

Noise Sensitivity of Boolean Functions and Percolation

2015 ◽  
Author(s):  
Christophe Garban ◽  
Jeffrey E. Steif
Keyword(s):  
Boolean Functions ◽  
Noise Sensitivity

CLASS OF BOOLEAN FUNCTIONS CONSTRUCTED USING SIGNIFICANT BITS OF LINEAR RECURRENCES OVER THE RING ℤ2n

2019 ◽  
Vol 6 (2) ◽  
pp. 90-94
Author(s):  
Hernandez Piloto Daniel Humberto
Keyword(s):  
Linear Function ◽  
Boolean Functions ◽  
Hamming Distance ◽  
Linear Recurrences ◽  
Maximum Period ◽  
Non Linear ◽  
The Given ◽  
Class Of Functions

In this work a class of functions is studied, which are built with the help of significant bits sequences on the ring ℤ2n. This class is built with use of a function ψ: ℤ2n → ℤ2. In public literature there are works in which ψ is a linear function. Here we will use a non-linear ψ function for this set. It is known that the period of a polynomial F in the ring ℤ2n is equal to T(mod 2)2α, where α∈ , n01- . The polynomials for which it is true that T(F) = T(F mod 2), in other words α = 0, are called marked polynomials. For our class we are going to use a polynomial with a maximum period as the characteristic polyomial. In the present work we show the bounds of the given class: non-linearity, the weight of the functions, the Hamming distance between functions. The Hamming distance between these functions and functions of other known classes is also given.

On the Signal-to-Noise Ratio for Boolean Functions

2020 ◽  
Vol E103.A (12) ◽  
pp. 1659-1665
Author(s):  
Yu ZHOU ◽  
Wei ZHAO ◽  
Zhixiong CHEN ◽  
Weiqiong WANG ◽  
Xiaoni DU
Keyword(s):  
Boolean Functions ◽  
Signal To Noise Ratio ◽  
Signal To Noise ◽  
Noise Ratio

Balanced Boolean Functions of σƒ>22n+2n+3(n≥4)

2015 ◽  
Vol E98.A (6) ◽  
pp. 1313-1319
Author(s):  
Yu ZHOU ◽  
Lin WANG ◽  
Weiqiong WANG ◽  
Xiaoni DU
Keyword(s):  
Boolean Functions
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