Merab Pkhovelishvili

A method of fast parallel information retrieval is proposed - the wave method . Representation of trees using lists in functional programming languages and modern search implementations.

The automatic programming system has been considered by means of which it becomes easier to

carry out traditional programming stages. There is discussed both recursive forms: parallel, interrecursion and

recursion of high level that exist for functional programming languages and induction methods for the purpose of

their verification. The way how to present imperative languages easy and double cycles by means of recursion

forms is shown, the possibility of verification has been studied for each recursion form.

The article discusses the problems of proving the correctness of programs for functional programs. For these purposes, a recursive generalized form of lisp programs is given, which makes it possible to verify or prove the incorrectness of the checking programs.

The method of verification offered by us is mainly applied for the functional languages.However, considering that the majority constructions of these languages are reducible for the constructions of the functional languages, the same methods can be applicable for the verification of the imperative languages.

We propose an approach to program verification that is universal in the sense that it can be used for both functional and imperative paradigm languages

is deemed to be the highly practical one

The synthesis problems for recursive functions based on the program examples are discussed. The new algorithm of the Automated Synthesis System (ASS) is presented, which

synthesis problems for recursive functions based on the program examples are discussed. The new algorithm of the Automated Synthesis System (ASS) is presented, which

is deemed to be the highly practical one. In the beginning, two examples are presented and

the differences are calculated between the arguments and results.

The structure of recursive forms of functional programs is investigated. Two main generalized forms for automatic program synthesis are defined

 During the recent years, creation of parallel secure

programs has become one of the main goals since microprocessors are no more a rarity. Functional languages are

assisting us to keep up the parallelism enabling inclusion of

unchangeable structures of data, which can be transferred

between streams and computers, even without additional security

for the streams or atomic access. Besides, functional languages

simplify creation of libraries, supporting parallel processing (for

example, asynchronous working streams F#). In this article we

consider the information on trees and main operations: finding

elements in the tree, inserting and removing elements and also

traversing the tree by means of two programming languages F#

and C#. We will compare calculation process time parameters.

the features of the application of the Model Checking the presence of functional programs are considered

The planning process presented in the article is very similar to the verification process.

The description of the system is a finite set of states and transitions, as well as the description

of the property being checked is the input to the verification system. The verifier either concludes that the specified

property is executed, or, if it is not executed, it gives a counterexample - such a path from

the initial state on which the property is not executed.

including information in the Georgian language

The need for natural language interfaces for the database has become increasingly 

The issues of verifying parallel programs for functional languages using Kripke schemes are discussed.

The possibilities of reflecting parallelism in Kripke schemes are shown, which gives the ability to solve verification problems for parallel programs

Parallel programs are Verification using clusters. Developed form of claspsfunctionaliru for parallel applications

The technologies of traditional parallel programing MPI (Message Passing Interface) and OpenMP will be discussed, in addition the role of these technologies and inabilities. The directions of modern parallel programming which appeared by using functional languages will be presented. The parallelizing of the programs using competition will be reviewed.

In this paper, using the example of Haskell, we consider templates for infinite

data structures. Infinite data structures can be defined based on infinite lists,

and a recursion mechanism can also be used. Recursion in this case is used as

an appeal to recursive functions. The third way to create infinite data structures

is to use infinite types. This last method is the most

interesting for us. In the Haskell language, the data keyword is used to define recursive types

, which makes data structures of such types potentially infinite

The features of parallel programming in the Haskell language are considered. To organize parallel computing, two constructions have been introduced into the language that provide explicit

control. The combinator par, receives two parameters that are functions executed in parallel. The expression p ‘par‘ e has a value defined by e. In addition,

the construction indicates that p can be executed by a new thread parallel to

the parent thread continuing the execution of e. Support for "lazy" calculations imposes its own specifics on parallelism. It is believed Hat the function p can be executed

then, when its result is required. In this case, an additional thread will be created

A “small delay” algorithm 

This article discusses a new efficient sorting algorithm using parallel programming, which is referred to as

The article discusses a new approach to difficult-to-predict events. For this reason, the so - called parallel data is used-data of different types of precursors, which with a certain probability predict a certain single event. The gradual, "live" mode of operation of the forecasting process is also considered. The use of parallel data allows large supercomputers to be used not only for their original purpose - for large volumes of calculations, but also for processing parallel data in "Live" mode and as the main tool of the parallel data paradigm.

The article discusses the development of two algorithms operating on this principle-the Transponated ribbon algorithm for sorting (“equilateral”) and Matrix Multiplication.

The article discusses the development of two algorithms operating on this principle-the Transponated ribbon algorithm for sorting (“equilateral”) and Matrix Multiplication.

The main principle of the parallel algorithm proposed by us is: the division of data into parts and processing of nuclei should be done in parallel, thus minimizing the waiting of nuclei.

The new approach created for forecasting is discussed. The main essence of which lies in the joint use of the existing forecasting methods on supercomputers in real time and in the selection of several models for achieving the given goal from the existing models, the joint probability of which gives the best result. The practical application of this approach to solving such problems as earthquake forecasting and economics is discussed

The article discusses a new approach to Business Forecasting tasks, which implies the use of parallel data paradigm in programming. Parallel data are different types of forward data that predict a certain single event in a dynamic mode. Also, step by step, online operation of the forecasting process will be discussed. The presented method allows supercomputers to be used not only for their original purpose - for large volumes of calculations, but also for online processing of parallel data, and also to be used as the main tool of the parallel data paradigm.

On the basis of parallel data theory, the issues of prediction of events are discussed. The data to be used form a heterogeneous matrix, the question of determining universal elementary operations on heterogeneous types of data is discussed

The possibility of solving problems arising when using different types of forecasting systems on modern supercomputers simultaneously is discussed. In particular, the new nontraditional is considered, The Matrix where there are homogeneous data in the columns, but not necessarily numbers. When performing operations on matrices, there is a question of the necessity of determining new(extended) operations on heterogeneous data. New operations on texts are introduced. On numbers and texts, and a.Sh. Subsequently, it is possible to perform various operations on the equilateral matrices (addition, multiplication, comparison, etc.).), Which makes it possible to solve some complex tasks in mathematics.

A new approach to the events, which are difficult to predict is considered in the article. For this so-called parallel data is used - data of various precursors, by means of which the certain event is predicted with some low probability. A "live" functioning of prediction process is also reviewed. Using of parallel data allows to use supercomputers not only for their initial purpose - performing many computations of high volume, but also for "live" processing of parallel data and as a main instrument fundamental style of parallel data.

Construction of much more efficient new hybrid models using parallel data from predictive models is considered. The algorithm for choosing pairs of models and its advantages over any of the best models for forecasting are given. The advantage of the pairs of the larger number of prediction models over the smaller number of pairs is shown and the algorithm for taking into account the "approximate coincidences" of forecasts when choosing pairs is considered

Management or avoidance of risks or mitigation of undesirable outcomes are linked to specific actions, as well as to prediction models. These prediction models should be improved to obtain ‚better‛ predictions and thus, manage risks, and take measures for their reduction. We consider such algorithm of event prediction, which, using parallel data, can obtain prediction with high reliability that, in its turn, helps to reduce risks or completely avoid them

The article discusses the issues of improving existing forecasting models, for which parallel data are used. These are data that simultaneously influence the prediction of any event. The article describes the following stages of the application of this method: delimitation of the accuracy of the prediction by depicting the forecasts of the elements of the object in the equilateral space and the algorithm for calculating the error in this space between them, and an improved algorithm for using parallel data in dynamic forecasting tasks.

Doctoral Thesis Referee

Master Theses Supervisor

Doctoral Thesis Supervisor/Co-supervisor

Scientific editor of monographs in foreign languages

Scientific editor of a monograph in Georgian

Editor-in-Chief of a peer-reviewed or professional journal / proceedings

Review of a scientific professional journal / proceedings

Member of the editorial board of a peer-reviewed scientific or professional journal / proceedings

Participation in a project / grant funded by an international organization

Participation in a project / grant funded from the state budget

Patent authorship

Membership of the Georgian National Academy of Science or Georgian Academy of Agricultural Sciences

Membership of an international professional organization

Membership of the Conference Organizing / Program Committee

National Award / Sectoral Award, Order, Medal, etc.

Honorary title

Monograph

Handbook

Research articles in high impact factor and local Scientific Journals

Publication in Scientific Conference Proceedings Indexed in Web of Science and Scopus