StatusThe thesis was presented on the 14 May, 2019
Approved by NCAA on the 6 December, 2019
Abstract– 0.30 Mb / in romanian
– 0.30 Mb / in english
0.77 Mb /
Thesis structure: the thesis is written in English and consists of: introduction, four chapters, general conclusions and recommendations, 200 bibliography titles, 116 pages of main text. The obtained results were published in 20 scientiﬁc papers.
Domain of research: Distances on abstract algebraic structures.
Goals and objectives: The goal of the research is to study the problem of distances on free monoids. To achieve this goal, the following objectives were deﬁned: elaboration of an effective method for extending the quasi-metric on free monoids; development of efgicient representations of information for data analysis; implementation of innovative algorithms for solving text sequences problems; describe digital topologies on the discrete line.
The scientiﬁc novelty and originality consist in obtaining new theoretical results with applications in computer science. An eﬀective method of distance extension on free monoids was developed, which helped to introduce the concept of parallel representation of information. This has allowed the development of the concepts of eﬃciency and similarity of the information sequences, as well as the construction of the sets of weighted mean and bisector of strings.
The important scientiﬁc problem solved in the research is the development of methods for constructing and studying distances on free monoids, which contribute to obtaining effective methods of representing information, applicable to solving diﬀerent distance problems.
The theoretical signiﬁcance is determined by the obtaining of the new results regarding the establishment of the conditions of existence of the extension of the distance on free monoids. The elaborated methods have allowed to approach the problems related to information sequences from a new point of view. New algorithms of constructing strings weighted mean and bisector were proposed. It has been established that the informational segment is not convex.
The applicative value of the paper consists in the use of the obtained theoretical results in the study of symmetric topologies on the digital line, imaging processing and construction of the centroid of a set of strings.
The implementation of the scientiﬁc results. The obtained results can be used in scientiﬁc research related to data analysis, the study of the eﬃciency of information representation, digital image processing. They can also be used in development of an optional course for university students related to the study of distances on abstract algebraic structures.
Under consideration  :