Study the possibility of using homomorphic computing to organize confidential calculations, including the development of a model for cloud computing privacy using homomorphic threshold calculations. Study the algorithmic complexity of solving equations in the semigroup of finite permutations of the first order.
The aim of the project is to study various generalizations of the problem of unification and anti-unification of algebraic terms, the estimation of complexity and development of efficient algorithms for solving these problems, the study of formal models of programs in order to select those models in which the problem of detecting the similarity of programs is reduced to the problems of verification of equivalence and minimization programs атв also to the problems of unification and anti-unification of algebraic terms.
The main aim of the project is to create software tools that allow more efficient use of computing resources in the cloud. The results are applied in the system UniHUB for hosting applications on virtual machines running OpenStack.
Different methods of analysis of random graphs, construction of new mathematical models of scale-free graphs (conforming the so-called power law) is a topical area of research concerning the analysis of networks on the Internet (in particular, social networks such as Facebook, Twitter and many others). However, the properties and parameters of these networks can change. To predict such changes it is necessary to study the general properties of mathematical models of such networks which can be considered as random graphs.