Diana S. Davidova

Diana S. Davidova
University of Bergen | UiB · Department of Informatics

Doctor of Philosophy

About

11
Publications
790
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5
Citations
Additional affiliations
February 2014 - present
European Regional Academy
Position
  • Lecturer
Description
  • Group Theory, Number Theory, Linear Algebra, Mathematical Logic
October 2009 - December 2010
Yerevan State University
Position
  • young researcher
Education
November 2010 - November 2012
Yerevan State University
Field of study
  • Mathematics

Publications

Publications (11)
Article
Full-text available
Boolean functions, and bent functions in particular, are considered up to so-called EA-equivalence, which is the most general known equivalence relation preserving bentness of functions. However, for a special type of bent functions, so-called Niho bent functions there is a more general equivalence relation called o-equivalence which is induced fro...
Preprint
Full-text available
The six infinite families of power APN functions are among the oldest known instances of APN functions, and it has been conjectured in 2000 that they exhaust all possible power APN functions. Another long-standing open problem is that of the Walsh spectrum of the Dobbertin power family, which is the only one among the six families for which it rema...
Article
Full-text available
We give set-theoretical characterizations both for weakly idempotent lattices and interlaced weakly idempotent bilattices. In particular, we obtain a set-theoretical representation for interlaced bilattices and distributive bilattices (without bounds).
Conference Paper
A hyperidentity is a second order universal formula, i.e., a universal formula from the second order language (in the sense of A. Church and A.I. Mal'tsev). The hyperidentities of the variety of weakly idempotent lattices are completely characterized in this paper. The existence of a finite base of hyperidentities for this variety is proved as a co...
Article
Full-text available
In this paper we study weakly idempotent lattices with an additional interlaced operation. We characterize interlacity of a weakly idempotent semilattice operation, using the concept of hyperidentity and prove that a weakly idempotent bilattice with an interlaced operation is epimorphic to the superproduct with negation of two equal lattices. In th...
Chapter
Full-text available
In 2008 Budaghyan, Carlet and Leander generalized a known instance of an APN function over the finite field \(\mathbb {F}_{2^{12}}\) and constructed two new infinite families of APN binomials over the finite field \(\mathbb {F}_{2^n}\), one for n divisible by 3, and one for n divisible by 4. By relaxing conditions, the family of APN binomials for n...
Article
Full-text available
The variety of weakly idempotent lattices is a nilpotent shift of the variety of lattices. In this paper the hyperidentities of the variety of weakly idempotent lattices are characterized.
Article
Full-text available
In the present paper, we consider the concepts of q-semilattices, q-lattices, and q-bilattices with unary operation and prove the existence of an epimorphism between q-bilattices of some varieties and the superproduct of two lattices.
Article
Full-text available
In this paper the concept of q-bilattice is studied. Interlaced q-bilattices are characterized by the pair of congruencies. Keywords: q-semilattice, q-lattice, q-bilattice, an interlaced q-bilattice, hyperidentity.

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Projects

Project (1)
Project
The structure theory of idempotent and weakly idempotent algebras and varieties with hyperidentities is develop.