A General Theory of Applied Algorithms

A General Theory of Applied Algorithms

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.

https://www.researchgate.net/publication/391768843_A_Novel_Approach_Leveraging_a_General_Theory_of_Applied_Algorithms_for_High-Level_Language_Design

P.S. It is highly improbable for such languages to emerge solely by experience and intuition, similar to the languages that were developed during the early stages of the information age. The development of high-performance languages requires the application of theoretical principles.

P.P.S. In this work, for the first time in the field of information technology, I give a description of the structure of the General Theory of Applied Algorithms - a list of the attributes of a theory. Even if the theory I propose is unfinished or false, researchers receive a model of the theory and the direction of its development.

Valery Kolesnyk
20.05.2025