System Of Algorithmic Algebras Research Articles

УДОСКОНАЛЕНА МОДЕЛЬ ПАРАЛЕЛЬНОГО АЛГОРИТМУ СОРТУВАННЯ З ФОРМУВАННЯМ РАНГІВ

The model of parallel sorting of a number array with ranking based on the simultaneous application of high-speed decrement/increment operations according to the array of numbers and the array of their ranks is improved. Acceleration of the proposed algorithm is achieved by fixing the result of zeroing (n -1) elements of the number array instead of its complete zeroing. The description of the algorithm of parallel sorting with the formation of ranks in a compact form using the basis of Glushkov’s system of algorithmic algebras (SAA) is given. Keywords: system of algorithmic algebras, parallel sorting, mask, rank, decrement/increment.

PIONEER OF INFORMATION SCIENCE AND CYBERNETICS <i>ON THE 100TH ANNIVERSARY OF THE BIRTH OF ACADEMICIAN V.M. GLUSHKOV</i>

The article is devoted to the life and work of the outstanding Soviet scientist, pioneer of informatics and cybernetics, initiator of the development of a nationwide automated management information system, Academician of the Academy of Sciences of the USSR Viktor Mikhailovich Glushkov (1923–1982). The author tells about the main stages of his biography, focusing on the scientific achievements: the solution of the fifth generalized Hilbert problem, the creation of the USSR’s largest Institute of Cybernetics of the Academy of Sciences of the Ukrainian SSR, the development of the theory of digital automata, the first personal computers for engineering calculations, the most powerful supercomputers in the USSR with a new macro-pipeline architecture, contribution to cybernetics and computer science, programming theory and systems of algorithmic algebras, to the creation of artificial intelligence systems. Attention is paid to the role of V.M. Glushkov as an ideologist and one of the creators of the industry of management information systems in the USSR, scientific director of large industrial management information systems. Particular attention is paid to the National Automated System for the Collection and Processing of Information proposed by him for accounting, planning and management of the national economy.

Integration of the methods of algebra of algorithms and computational intelligence for automation of program systems design

An approach to the creation of intelligent systems is considered, which combines the ideas of Glushkov’s algebra of algorithms with the well-known neuroevolutionary algorithms of computational intelligence, which can be used to automate the design and synthesis of programs. The method of neuroevolution of augmenting topologies is intended to reduce the dimensionality of the space for searching for neural network parameters in the form of gradual development of its structure in the process of evolution. A software toolkit has been developed to support the approach, which is based on the construction of high-level specifications of algorithms represented in systems of algorithmic algebras, and generation of corresponding programs based on implementation templates in a target programming language. Parameterized algorithms called hyperschemes are used to solve a certain class of problems. Setting specific values of parameters and subsequent interpretation of hyperschemes allows obtaining algorithms adapted to specific application conditions. The developed program design and synthesis toolkit provides step-by-step development of programs, starting from a high-level algebraic-algorithmic specification. At the output of the toolkit, a program is automatically generated in one of the target programming languages (С, С++, Java, Python), that also include a subject-oriented language for designing neural networks. The mentioned language includes operators and conditions for working with populations, configurations, genomes, and fitness function. The work of the toolkit is illustrated by the example of designing a parameterized evaluation algorithm for a binary multiplexer and generation of a program for the single-pole balancing problem

Methods of Ordering in Computer Sciences and Information Technologies

The purpose of the article is to analyze the known methods of ordering in computer science. The research methodology consists of methods of ordered pairs, relations, Gödel numbering, and Glushkov’s system of algorithmic algebras. The scientific novelty is to create a method of both description and transformation of orders. Conclusions. In the methods of ordered pairs, relations, Gödel numbering, mathematical logic, Post and Turing machines, and the modified system of Glushkov’s algorithmic algebras there is no possibility of equivalent transformations of orders which are available in algorithms.

Modeling and Verification Methods for Application Design in Heterogeneous Architectures

A methodology of application design for massive parallelism systems on the example of GPGPU systems focused on the algorithmic design stage is proposed. Two stages of design are considered: creation of a formal specification and its research and verification. For the first stage, the use of mathematical apparatus of the system of algorithmic algebras/modified system of algorithmic algebras and transition systems is proposed. For the second stage, the use of network and automatic models is analyzed, and the advantages of each model are given. In particular, the computational model in NVIDIA CUDA using Petri nets, as well as the linear-temporal logic formulas and automatic model, was studied.

Formalization of the Object Classification Algorithm

An algorithm for object classification using the criterion of the maximum of discriminant functions is considered. A special feature of this algorithm is parallel processing over the columns of the matrix that consists of elements of discriminant functions. This algorithm is represented in terms of Glushkov's system of algorithmic algebras.

Data based algorithmic algebra

A system of algorithmic algebras is formed on the basis a modified Glushkov computer model. Data are formalized and specified at inputs and outputs of D-operators and, hence, the formal apparatus constructed is based on data. Some properties of D-operators and operations that form the signature of the algebras are proved and the possibility of construction of derived D-operators is shown.

An approach to the parallel solution of a high-dimensional basic flow problem

The body of mathematics of modified systems of algorithmic algebras (SAA-M) is used to formalize the Edmonds---Karp algorithm of finding the maximum flow in a network. With allowance made for the distributed system features that are usually used for solving complicated problems, optimization criteria are formulated and used to obtain parallel SAA-M-schemes.

Formalization of interrelations between operators and data within the framework of an extended algebra of algorithms

A system of algorithmic algebras is considered whose basic concepts are newly interpreted to formalize the interrelation between operators and data of such a system. A modified formal instrument is constructed that extends the possibilities of design and transformation of regular schemes of algorithms.

Formation and Development of Ideas of Artificial Intelligence in V. M. Glushkov’s Works

Ideas and means of artificial intelligence are considered that are developed in works of V. M. Glushkov and are used in brain modeling, computer-aided training, automata theory, and systems of algorithmic algebras.

Issues of algorithmics and glushkov’s systems of algorithmic algebras

Issues of algorithmics and glushkov’s systems of algorithmic algebras

A methodology of structured-modular composition programming

Development and implementation of programming technologies require highly efficient software design methodologies and a mathematical apparatus for verification of software systems. An important role in this context is associated with the design of application systems as an efficient tool for supporting computerized knowledge acquisition technoliges in various subject domains. Widely used and fairly advanced are design methodologies based on the procedure-oriented approach, which are used to solve specific programming problems. In particular, the composition methodology provides a tool for the construction of program models that match the functional requirements of the programs and reflect the adaptation of programs to specific applications. The formal apparatus of this methodology is based on the composition algebra. The methodology of multilevel structured program design is used for formalized design of algorithms based on modified systems of algorithmic algebras as the formal apparatus. The structured methodology combined with the formal apparatus of the system of algorithmic algebras satisfies many requirements at its time and was used for the construction of numerous software-technology systems. We accordingly expect that the creation of a generalized methodology that includes methods for the construction of single programs as well as methods for the construction of whole software systems and organicallymore » combines the most important aspects of known programming methodologies, followed by the development of a qualitatively new mathematical apparatus for the programming formalism will elevate programmology to a qualitatively new level of progress. The first steps made by the authors in this direction confirm the efficiency and potential promise of the approach. The present article generalizes the authors` results in this direction.« less

Deadlock and fictitiousness problem in parallel program specifications

One of the directions of modern programming based on algebraic methods takes its origin in V.M. Glushkov`s theory of systems of algorithmic algebras (SAA). The SAA apparatus with appropriately interpreted operations is used for program design and allows compact structured representation of program schemas in the form of algebraic formulas. Modified systems of algorithmic algebras (SAA-M) additionally represent parallelism description tools.

Formalization of software design for process control systems in ferrous metallurgy

The operation of control systems in bar-rolling mills is examined and software design tools for such systems are proposed. A system of algorithmic algebras for these design tools is constructed and its capabilities are considered.

Some aspects of the design of local process-control systems

Some aspects of the software for one class of industrial process control systems are considered. A system of algorithmic algebras is proposed, adapting the structured program design method to this particular class of control systems.

Algebraic-grammatical specifications and synthesis of structured program schemas

The paper proposes hierarchical specifications of classes of algorithms and programs (both sequential and parallel) in algebras of hyperschemas (AHS), based on Glushkov's systems of algorithmic algebras. Derivation-control algorithms for various grammatical models are presented in AHS.

On some classes of algorithmic algebras

Two classes of algorithmic algebras are studied: S*-algebras, which are a direct generalization of S-algebras (algebras with closed conditions), and Markov systems of algorithmic algebras (a stochastic version of algorithmic algebras).

Structured programming in symbolic multiprocessing

This article applies Glushkov's systems of algorithmic algebras (SAA) to symbolic multiprocessing. Regular schemata on abstract memory types are used to formalize the main control techniques for parallel computations in slipway and pipeline multiprocessing. The expressive power of the proposed SAA apparatus is demonstrated for the reader-writer problem, the dynamic communication problem, the firing line problem, and parallel parsing. Structured design grammars combining the SAA apparatus with formal language models are applied for direct and inverse transformation from synchronous to asynchronous regular schemata and back. It is determined that program design based on structured design grammars preserves all the advantages of structured programming and enables partial program verification using top-down, bottom-up, and mixed parsers, the optimization of programs by prespecified criteria using the apparatus of identity transformations developed within the framework of SAA theory, and the joint multilevel (top-down, bottom-up, and mixed) design of structured algorithms and programs.

Solvability of equivalence problems in a system of algorithmic algebras

Solvability of equivalence problems in a system of algorithmic algebras

Problem of identity transformations of nondeterministic program shcemes in algorithmic algebra systems

Ever-increasing attention to the investigation of nondeterministic processes that generalize deterministic processes because of elimination of the rigidity of execution inherent in the latter is characteristic of modern programming. Nondeterminism reflects the crux of the sampling problem in tasks allowing multivaluedness of solutions such as automation of the proofs of theorems, syntactical and semantical models of languages, distribution of resources in multiprocessor computer systems and time-sharing systems, etc. Nondeterminism is used in proving any assertions about programs by means of the apparatus of program logic that occur and are developed on the junction of mathematical logic and the theory of programming. The systems of algorithmic algebras (SAA) proposed by Glushkov (1956) and adequate conceptions of structural programming are the fundamental basis of propositional program logic. In the interests of orientating the SAA apparatus in the formalization of parallel calculations, their signature was expanded by including filtration and parallelism operations. The algebraic systems obtained in this manner were called modified SAA. Identity problems and axiomatization by using a single deduction rule, the traditional formulation, were solved by Tseitlin (1974) for s(o)-algebras modified by SAA with closed logic conditions. In this paper, the mentioned results are extended to the case of s(h)more » algebras, SAA with closed logic conditions, in whose signature the parallelism operations are replaced by nondeterministic disjunction operators. 9 references.« less