1. The decomposition scheme theory as a prototype of the theory of applied algorithms. The paper copy of the article is in the library and in the magazine.
The notion of the decomposition scheme as a
core for decomposition scheme theory is proposed and described
here. The notions of clump-property and algorithmic dependence are also
described. Decomposition scheme is proposed to be used taking into account its
algorithmic nature as the basis for building universal (canonical) algorithm.
The questions of the canonical algorithm transformation into the specific
application-oriented algorithms are discussed. The operations over the
decomposition schemes which are itself operations over algorithms are
described.
The full text of the article
here. (In Russian)
https://pp.isofts.kiev.ua/index.php/ojs1/article/view/35
To read the article that describes the generic algorithm model, please go to the link. The article is in English. It is not a professional translation for which I apologize.
To read the article (which was published second) that describes how a generic algorithm model transforms into a program text in a standard algorithmic language, please go to the link. The article is in English. It is not a professional translation for which I apologize.
https://docs.google.com/document/d/1jUK3IhIPHSLIfLi2sF1ONpNawLnUBJ_6/edit?usp=drivesdk&ouid=105725534057286965327&rtpof=true&sd=true
2. The decomposition scheme theory. Presentation of canonical algorithm by means of algorithmic language The paper copy of the article is in the library and in the magazine.
This work continues the description of the
decomposition scheme as a theoretical model, which makes possible
generation of the applied algorithms. The description of the algorithmic
language made for show the possibility of algorithms generation is given. One
of the factors' group is described, i.e. ways of placing the properties on the
tape of the abstract type which when is taken into consideration allows to turn
canonical algorithm into a real one and applied algorithm, which is the
same as turning the decomposition scheme into the program
text. The notions of algorithmic primitive and algorithmic joint
(operand and operation) as the means for constructing the algorithm are
introduced. These notions of algorithms construction are the
alternatives for the notional system and methods of structured programming. The
notions of functional core, algorithmic frame, functional contents and
algorithmic matrix are introduced.
The full text of the article here. (In Russian)
To read the article that describes how a generic algorithm model transforms into a program text in a standard algorithmic language, please go to the link. The article is in English. It is not a professional translation for which I apologize.
3. The decomposition scheme theory. Research of R-data division factors in order to generate applied algorithms The paper copy of the article is in the library and in the magazine.
R-data kinds of division are described and factors of
their fragments and components placing are considered. For all the variants of
R-data division the changes into the canonic algorithm which are necessary for
their union are described. From the standpoint of the complexity changes in
algorithm vary from primitives in several imperative operators to algorithmic
constructions with loops and control constructs. For making the algorithmic
constructions there is the mechanism of synthesis offered – bound to the levels
of algorithm tree. For purposes of the comparative analysis the schemes of
decomposition and applied algorithm there was offered the notion of
NAC-conditionality as more fitting that the graph isomorphism. It is shown that
description of the variants and factors of R-data division is declarative.
The full text of the article is here and here. (In Russian)
https://pp.isofts.kiev.ua/ojs1/article/view/209
https://pp.isofts.kiev.ua/index.php/ojs1/article/view/155/149
4. The decomposition scheme theory. The research of R-data factors formatting for algorithms generation The paper copy of the article is in the library and in the magazine.
This work continues the presentment of the
decomposition scheme theory as the theory of applied algorithms. The
mechanism of conversion of a decomposition scheme into a real applied algorithm
conditioned by the variety of data storage forms on the data carriers has been
considered. Data storage portion as a phenomenon of electronic data processing
has been described and there has also been suggested a general concept of a
storage portion. The factors which generate the need for formatting and
reformatting the data have been described. Generalized picture of data
formatting has been given. The group of algorithmic constructions which realize
the procedures of formatting and reformatting of the data for the general case
has been suggested. The fact that within the theory of the decomposition
schemes there exist considerably more circumstances of combining and
cooperation of the storage portions than described in this work has been
clarified. The mechanism of the canonic algorithm and synthesis of the
algorithmic constructions which realize the procedures of data formatting has
been suggested. The process of putting changes into the canonic algorithm is
logical and methodic.
The full text of the article is here. (In Russian)
https://pp.isofts.kiev.ua/ojs1/article/view/209
5. The decomposition scheme theory. Scientific aspects and prospects for development
The work presents the decomposition scheme theory as a scientific theory. Its attributes has been described – paradigm, field of research, aim of research, main task, decision method, basic theory model – decomposition scheme. Practical aim of the theory is to suggest the mechanism of applied algorithms generation (not machine code). It is shown that the decomposition scheme as a description changes the algorithm description and still remains declarative on the contrary to the algorithm description as imperative. With this the decomposition scheme is the description, original for algorithms’ generation. The kinds of decomposition schemes and operations on them have been described. Algorithmically relevant factors which should be considered when generating algorithms in order the algorithms turned real have been described. Working over formalization and mathematical description of the phenomena and objects of the theory of the decomposition schemes has been described here. The mechanism for control of conclusions and results of the theory has been suggested. This work also describes the direction of development of the theory of the decomposition schemes. The priority direction relates to the creation and development of the system of capacious notion and abstractions. From the point of view of the practical application of the theory of the decomposition schemes there has been suggested the approach which is alike to the one used in machine-building – development and promoting of hi-tech when required – as a result of the targeted research.
The full text of the article is here. (In Russian)
https://pp.isofts.kiev.ua/index.php/ojs1/article/view/218
6. On the possibility of a systematic study of the production management systems
Degree of similarity between systems, subsystems and tasks of MIS for different industries (the companies, departments, shops) is minimum that generates big expenses in designing of the software. The methodology of designing of MIS hides significant reserves for essential reduction in cost of these works. The purpose of this work is in offering the generalized (unified) scheme of tasks or subsystems of MIS that will allow to reduce costs for their designing. The conceptual model of the production management system is offered as such scheme. Basic managerial system with a cluster of models of the simplest production systems, managerial system tree, planning feature, function of cost accounting and the idea of polyfunctionality of production information is attributes of the conceptual model. The method of representation of multi-level a production management system as superposition of two-level managerial systems is offered. Two ideas – cluster of models of the elementary production systems and superposition of managerial systems – create prerequisites for classification and typification of the production management systems. The organizational mechanism and the mechanism of aggregating of production information are objects of a first-priority research among attributes of model of the elementary production systems. Classification and typification of the production management systems are a necessary condition for creation universal (or quasi-universal) the conceptual model of the production management system. The conceptual model of the production management system is considered as a basis for MIS designing.
The full text of the article is here. (In Russian)
https://pp.isofts.kiev.ua/index.php/ojs1/article/view/319/314
7. Formalization of the decomposition process
The article is devoted to the formal description of the procedure and scheme for the decomposition of arbitrary objects: objects, phenomena, organisms, processes in animate and inanimate nature. Attributes of the decomposition scheme such as an object property; various types of dependencies that can bind the properties of an object; decomposition mechanism; a graphic representation of the decomposition scheme — given and formally described. Varieties of decomposition schemes such as division decomposition and decomposition with inclusion are described. The variety of decomposition schemes and the variety of decomposition mechanisms are shown. The action of various variations of the decomposition scheme, such as: the scheme for the formation of new knowledge of the studied objects; design and production scheme for new objects: artifacts and processes; a scheme for transforming objects: modernization, reorganization, reforming, repair, etc. - formally described. A formal description is considered as a prerequisite for the analysis and synthesis of complex objects and complex systems at a level comparable to the level of mathematical accuracy and rigor. The synthesis and design of various multifunctional equipment, various multifactorial processes, objects and processes of art, and, in particular, systems of the IT industry - is implied. For the first time introduced and formally described the concepts “type of property” and “algorithmic dependence”. Algorithmic dependence exists between types of properties. These two concepts are prerequisites for the creation and development of the theory for Software Engineering. The article mentions a similar theory. Operations with decomposition schemes are described. Most of the concepts and ideas are illustrated with examples from various fields of human activity. This is evidence that the scheme of decomposition and the process of decomposition is a general scientific and philosophical phenomenon. The idea of a decomposition scheme can provide effective interdisciplinary communication.
The full text of the article is here. (In Ukrainian)
https://visnukpfs.dp.ua/index.php/PFS/article/view/1020/1449
8. SYNTHESIS THEORY IN ACTION: DEDUCTIVE DERIVATION OF ALGORITHMS FOR APPLICATION SOFTWARE
Abstract. The significance of the study is contingent upon two criteria. All objects in the actual world that can capture a researcher’s attention are inherently complicated. Furthermore, every commodity that an individual manufactures and every work of art that an individual develops are intricate in nature. The entirety of the processes that an individual perceives and instigates are intricate. Although many professions have established techniques for constructing intricate entities, there currently exists no universally applicable concepts or methodologies for comprehensively studying, designing, producing, or generating complicated items.
The objective of this work is two-fold: firstly, to develop a comprehensive methodology for analysing complex synthetic processes, and secondly, to propose universal models or synthesis mechanisms that can be used to systematically derive specific process synthesis algorithms for various practical applications. The ability to utilize generalized models and synthesis techniques is highly advantageous when designing realistic computer programming.
The authors introduced a comprehensive process model and enumerated its characteristics. Using this concept, techniques for creating and suggesting processes have been formulated and put forward. The concept of a decomposition diagram enables the systematic design of intricate multi-level hierarchical processes. The multitude of processes and the intricacy of their combination give rise to the notion of formulating a synthesis theory. The acquired results can be regarded as the initial stage in the construction of such a theory. The authors’ proposed methods of process synthesis enable the deductive derivation of useful algorithms for application software. Although the concept of the breakdown scheme and synthesis procedures is relatively straightforward, this advancement has been suggested for the first time.
In order to further this project, it is necessary to augment the generalized process model with supplementary traits and properties, as well as to further refine the synthesis procedures. A proposal is being made to initiate the development of a theory for synthesizing a comprehensive plan using the decomposition scheme and methods of synthesis and decomposition.
Key words: theory of synthesis, method of synthesis, scheme for decomposition, algorithm, deductive reasoning, algorithm synthesis.
The full text of the article is here. (In English)
https://visnukpfs.dp.ua/index.php/PFS/article/view/1137/1574
9. "Algorithmic Approaches to Universal Analysis Models".
The concept of analysis is being contemplated in its most comprehensive philosophical context. An endeavour is undertaken to systematise the examination and present it in the form of a systematic procedure, in essence, to construct a formal comprehensive analysis model. The generalised model combines normal data processing procedures with pairs of philosophical categories of the most generic form as components. The sequence of their application is determined. This order is based on the degree of generality of the categories. Consequently, several analysis models were acquired. Despite the observable consistency in the sequence of category application, a comprehensive analytical model has not yet been established based on this series. However, the analysis techniques that have been obtained can already be regarded as prototypes of practical algorithms, serving as the foundation for deductively deriving algorithms for actual computer programmes.
Keywords: analysis, algorithmic analysis model, analysis algorithm, generalized concepts, philosophical categories, system, element.
The full text of the article is here. (In English)
http://usim.org.ua/?page_id=16960&lang=uk
10. A Novel Approach: Leveraging a General Theory of Applied Algorithms for High-Level Language Design
Relevance of the work. Among researchers, software project managers and practicing programmers, there is an understanding that Software Engineering needs a productive theory. Despite the fact that certain efforts have already been made and are being made to create such a theory, the result has not been achieved. In Software Engineering, as in any technology, in addition to the programming process, there are many other processes and many different types of work. But it is the programming process that is the most labor-intensive and must be changed radically. Programming must be transferred to a higher stage of development - this is the main condition that can ensure progress in Software Engineering. In programming, languages of a different type are needed that will significantly reduce the detailing of the program text. But such algorithmic languages can only be obtained as a result of theoretical research.
Objective. The objective of this work is to describe the General Theory of Applied Algorithms (GTAA). The description of the theory involves defining the main attributes of the theory, namely, the research methodology, the field of research, the object of research, the subject of research, the main (basic) assumptions (axioms), the main task of the theory, the theoretical generalized model of the decomposition scheme as a method for solving the main problem, the research method, the purpose of research, the directions of research.
Research method. The paper uses the idea of the decomposition scheme and its attributes: the concepts of object type and object type property. The decomposition scheme is used to describe the solution of arbitrary problems. The use of the decomposition scheme involves its development and connection with the algorithms of applied problems.
Result. The paper defines and describes the above-listed attributes of the general theory of applied algorithms, introduces and describes the idea of virtual component operations (VCO). Such operations are well-known philosophical concepts such as decomposition, composition, deduction and induction. Within the framework of the theory, these operations are the imperative core, the further development of imperative operators that are in traditional algorithmic programming languages. Accordingly, VCO are used as building blocks for constructing the object property generation circuit. The object property generation circuit is a prototype of the algorithm and the application program.
Conclusion. The theory contains two main interrelated concepts: P-properties and VCO. They implement the idea of programming language operators with a high degree of generality. The theory creates prerequisites for designing a new type of programming languages that are significantly superior to existing languages.
The paper describes a complete decomposition scheme and an object property generation loop. These two constructions are considered together as a model of a universal or canonical algorithm.
The main task of the theory is to build a correct synthesis loop. The complete decomposition scheme and the synthesis loop are the initial data for generating an algorithm and an application program.
The article draws attention to the need for large-scale empirical research. The article provides references to the first works in this direction.
Key words. Decomposition scheme, object type, object part type, object properties, generalized programming concepts, algorithm.
...
The full text of the article is here. (In English)
==================================================
Valery Kolesnyk
May 2025
