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In the context of the approach given in Shannon's research ((Bell Syst. Tech. J. 28: 656––715, 1949)), of interest are the mixing properties of operations in a finite field, in particular, the action of each operation on cosets with respect to the action of the second operation. The good...
We consider the class of all n n single-valued mappings of an n -element set into itself. Assuming that all such mappings have the same probabilities equal to n ––n , we investigate the distribution of the random variable νν n equal to the number of connected components in such random...
We consider an asynchronous double stochastic flow with initiation of superfluous events (a generalised asynchronous flow), which is a mathematical model of information flows in computer networks, communication systems, etc. We study the stationary mode of the flow. We find the probability...
In this paper we study the average complexity of optimal algorithms solving the problem of searching for identical objects (PSIO) for random databases. We describe and investigate classes of PSIOs for which the average complexity as a function of the database volume grows logarithmically. For...
In this paper, we continue our studies concerning consistent sequences of tests in discrete probabilistic statistical schemes. We introduce the concept of a ‘‘prohibition’’ in a discrete probabilistic scheme and give a series of examples where ‘‘prohibitions’’ arise. In...
We suggest a new way to construct the structure of all closed classes of two-valued logic. In contrast to classical approaches, in this research the functions of two-valued logic are auxiliary objects and the construction starts from the set of predicates.
It is proved that the automorphism group of any commutative Moufang loop Q is an extension of the group F (1) consisting of all automorphisms of the loop Q which induce the identity mapping onto the factor-loop Q / A ( Q ) of Q by means of the automorphism group of the abelian group Q / A ( Q )....
In this paper we suggest a combined method for solving systems of Boolean polynomial equations based on testing a part of variables and using monomial compatibility criteria for dropping out some values of the tested variables. The complexity of the method is estimated for various parameters of...
We consider sets of graphs which are closed under the symmetric difference and renaming of vertices. We prove that for any n there are at most 14 such sets consisting of graphs with n vertices.
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