Creation and development of a general theory of applied algorithms

 

Creation and development of a general theory of applied algorithms

_____Problem. In mechanical engineering, designers and technologists usually consider drawings of new technical products at various councils. During the work of the council, drawings of the components of new products and the products themselves are hung on the walls of the room where the council meets. A two-dimensional image and uniform terminology allow specialists to delve into the essence of the design and mechanism within five to ten minutes. During the discussion, comments may be made regarding the design. Errors may also be noticed.

DSA-THEORY. PRESENTATION OF CANONICAL ALGORITHM BY MEANS OF ALGORITHMIC LANGUAGE

 

DSA-THEORY. PRESENTATION OF CANONICAL ALGORITHM BY MEANS OF ALGORITHMIC LANGUAGE

V.G. Kolesnyk

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.

Introduction

In [1], a description of a theoretical model called a decomposition scheme is given. It is also shown there that the decomposition scheme (DS) is of an algorithmic nature. In [1], the synthesis path (PS) and the canonical (universal) algorithm (CA) are described as the main attributes of the decomposition scheme.

DS-THEORY AS A PROTOTYPE OF THE THEORY OF APPLIED ALGORITHMS

 

DS-THEORY AS A PROTOTYPE OF THE THEORY OF APPLIED ALGORITHMS

V. G. Kolesnyk

The notion of the decomposition scheme as a core for DS-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.

Introduction

The notion of the decomposition scheme as a core for DS-theory is proposed and described here. The

Why do we need a General Theory of Applied Algorithms

 

Why do we need a General Theory of Applied Algorithms (GTAA)?

In Software Engineering, the craft style of production dominates. This means that design and production are mixed and performed simultaneously. Design is the creation of algorithms, and production is programming. That is, the creation of algorithms and programming are performed simultaneously. Sometimes, along with design and production, algorithm research is also performed. The stages of algorithm research, algorithm design and programming should be separated as it is in the industry: in mechanical engineering, in aircraft manufacturing, instrument making, etc. In the industry, the stages of research, design, technological preparation and production are separated and performed sequentially.

Algorithm Research

Research is carried out within the GTAA.

Algorithm research should be ongoing, similar to research in mathematics or other fields.

Research does not have to be associated with specific projects.

Research can be associated with specific projects.

Research processes and results should be presented in a concise, compact, and, if possible, simple language.

Research processes and results should not be presented in algorithmic language.

Algorithm Design

GTAA should be used for algorithm design.

The design language should be the same as for algorithm research.

Programming

The input to programming must be algorithms that are designed at the design stage.

Programming languages are used at the production stage, after the algorithms have been developed.

Problem

In order to achieve such a division of labor and move away from the craft style of programming, a theory and language are needed in which to conduct research and design algorithms.

Purpose of the GTAA language

The language is designed to describe the following phenomena.

– Stable (relatively unchanging) objects of the real world.

– Algorithms for research, studying stable objects, for observing them.

– Algorithms of real-world processes. Processes independent of the computer and interacting with the computer.

– Algorithms that are executed in the computer, in the network.

– Algorithms of interaction between man and computer.

Requirements for the GTAA language

The language must be strict, unlike natural language, and formal – as in mathematics.

The language must be a language of generalizations, as in mathematics.

The language must be graphical. More precisely, a hybrid of graphics and text with the prevalence of graphics.

The language must have a high degree of default.

The language must be focused on the description and depiction of algorithms.

The theory and language are based on a system of ontologies and philosophical procedures: decomposition, deduction, etc.

In theory and in language, mechanisms for synthesizing and analyzing algorithms must be researched and developed.

Requirements for programming languages

Programming languages must be specialized.

#General_Theory_of_Applied_Algorithms #GTAA

Valery Kolenyk

13/08/2025 

Changing the Approach to Problem Research in Software Engineering

Changing the Approach to Problem Research in Software Engineering

They say that if a problem is not solved, then you should change your perspective on the problem (view of the problem, approach to solving it). That's what I did. I changed my perspective on the process that occurs in a computer when it works according to a certain program. I began to consider this process in a broader context - a person cognizes (or changes) the world around him. Thanks to this, the understanding of the process changed.

 

Phenomenon	Traditional view	A Changed View
Process in a computer.	Information processing.	Generation (production) of knowledge – specific, applied information.
The smallest portion (atom) of processed information.	Data in digital, text or other form.	Element of knowledge. Construction “Subject is a predicate”. Concept from epistemology.
A program in text form.	Connection (concatenation) of operators of algorithmic language: imperative operator, conditional operator, cycle operator.	Connection of procedures (operators) decomposition, deduction, induction, composition etc.
Algorithm (structure) of a program.	Order of information processing.	Scheme (order) of generation (production) of knowledge.

 The change in approach allowed to construct universal schemes, which are prototypes of universal algorithms. The universal scheme is called a decomposition scheme. The decomposition scheme is the basic concept of the general theory of applied algorithms.

 Valery Kolesnyk

07.08.2025