Strong closure operators on the set of partial Boolean functions

2008 ◽  
Vol 77 (2) ◽  
pp. 288-289
Author(s):  
S. S. Marchenkov
Keyword(s):  
Boolean Functions ◽  
Closure Operators

scholarly journals The orbit of closure-involution operations: the case of Boolean functions

2021 ◽  
Author(s):  
Jürgen Dassow
Keyword(s):  
Boolean Functions ◽  
Closure Operator ◽  
Closure Operators ◽  
Repeated Applications

AbstractFor a set A of Boolean functions, a closure operator c and an involution i, let $$\mathcal{N}_{c,i}(A)$$ N c , i ( A ) be the number of sets which can be obtained from A by repeated applications of c and i. The orbit $$\mathcal{O}(c,i)$$ O ( c , i ) is defined as the set of all these numbers. We determine the orbits $$\mathcal{O}(S,i)$$ O ( S , i ) where S is the closure defined by superposition and i is the complement or the duality. For the negation $${{\,\mathrm{non}\,}}$$ non , the orbit $$\mathcal{O}(S,{{\,\mathrm{non}\,}})$$ O ( S , non ) is almost determined. Especially, we show that the orbit in all these cases contains at most seven numbers. Moreover, we present some closure operators where the orbit with respect to duality and negation is arbitrarily large.

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
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