Tuesday, November 25, 2025

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.

Monday, November 24, 2025

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