Summaries of articles of the decomposition scheme theory

1. The decomposition scheme theory as a prototype of the theory of applied algorithms. The paper copy of the article is in the magazine (here).

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 is here.   (In Russian)

2. The decomposition scheme theory. Presentation of canonical algorithm by means of algorithmic language. The paper copy of the article is in the magazine (is here).

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 is here.  (In Russian)

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 magazine (part one ­is here). The second part of the article is here.

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)

4. The decomposition scheme theory. The research of R-data factors formatting for algorithms generation. The paper copy of the article is in the magazine (is here).

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)

5. The decomposition scheme theory. Scientific aspects and prospects for development.  The paper copy of the article is in the magazine (is here).

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).