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Polynomial-delay construction of irreducible coverings of a Boolean matrix
      
Complexity of sequential implementation of partial Boolean functions
      
Multifunctional logic modules consisting of elements with bilateral conductance are proposed; when realizing Boolean formulas in the basis {>amp;amp;, v, !} consisting of at most six letters, these modules have no element redundancy.
      
Complexity of Boolean functions in intelligent systems for synthesis of digital integrated circuits
      
The representation of an arbitrary Boolean function over different bases in classes of formulas and circuits of functional elements (with and without branching) is considered.
      
A formal description of primal and dual greedy methods is given for a minimization version of the knapsack problem with Boolean variables.
      
The algorithm for finding this commonality is implemented by means of procedures on Boolean matrices with a sliding window and has been approved for the earthquakes in Kamchatka and the Kuril Islands.
      
Constructing irreducible coverings of a Boolean matrix
      
A polynomial delay algorithm for searching for irreducible coverings of a Boolean matrix is constructed.
      
A similar result is obtained for the problem of constructing maximal conjunctions of a monotone Boolean function specified by its conjunctive normal form.
      
The complexity of implementing a cyclic shift of a 2n-tuple of real numbers by Boolean circuits over the basis consisting of a ternary choice function and all binary Boolean functions is shown to be 2nn.
      
The p-weak isometries of the Boolean cube are considered, i.e., the mappings of the cube onto itself which preserve a fixed distance p.
      
Asymptotics of the probability of values of random Boolean expressions
      
This is an overview of the new possibilities that are open by Boolean valued analysis in positivity.
      
Finally, the 3D integrated model was established by Boolean operations between 3D geological objects and engineering objects.
      
Boolean functions of an odd number of variables with maximum algebraic immunity
      
In this paper, we study Boolean functions of an odd number of variables with maximum algebraic immunity.
      
We identify three classes of such functions, and give some necessary conditions of such functions, which help to examine whether a Boolean function of an odd number of variables has the maximum algebraic immunity.
      
Finally, we present a sufficient and necessary condition for Boolean functions of an odd number of variables to achieve maximum algebraic immunity and to be also 1-resilient.
      
By some basic transforms and invariant theory, we give two results: 1) an algorithm, which can be used to judge if two Boolean functions are affinely equivalent and to obtain the equivalence relationship if they are equivalent.
      
 

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