Construction of weightwise almost perfectly balanced Boolean functions on an arbitrary number of variables

2022 ◽  
Vol 307 ◽  
pp. 102-114
Author(s):  
Xiaoqi Guo ◽  
Sihong Su
Keyword(s):  
Boolean Functions ◽  
Arbitrary Number

scholarly journals On self-correcting logic circuits of unreliable gates

2021 ◽  
pp. 1-18
Author(s):  
Kirill Andreevich Popkov
Keyword(s):  
Positive Integer ◽  
Boolean Function ◽  
Boolean Functions ◽  
Arbitrary Number ◽  
Logic Circuits ◽  
Logic Circuit ◽  
Complete Basis

The following statements are proved: 1) for any integer m ≥ 3 there is a basis consisting of Boolean functions of no more than m variables, in which any Boolean function can be implemented by a logic circuit of unreliable gates that self-corrects relative to certain faults in an arbitrary number of gates; 2) for any positive integer k there are bases consisting of Boolean functions of no more than two variables, in each of which any Boolean function can be implemented by a logic circuit of unreliable gates that self-correct relative to certain faults in no more than k gates; 3) there is a functionally complete basis consisting of Boolean functions of no more than two variables, in which almost no Boolean function can be implemented by a logic circuit of unreliable gates that self-correct relative to at least some faults in no more than one gate.

Some properties of the inertia groups of Boolean bijunctive functions and an inductive method of generating such functions

2002 ◽  
Vol 12 (3) ◽  
Author(s):  
A.V. Tarasov
Keyword(s):  
Boolean Functions ◽  
Arbitrary Number ◽  
Inductive Method

AbstractThe class of bijunctive Boolean functions consists of the functions representable by the 2-CNF. The problem of enumeration of such function of arbitrary number of variables has not been solved. In the paper, we consider properties of inertia groups ofbijunctive functions in several groups and give an inductive method of generating all distinct representatives of the classes of geometric equivalence of bijunctive functions. By this method we calculate the numbers of bijunctive functions of 5, 6, and 7 variables.

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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