Synthesis-Analysis of Derivation Sequences of Tables’ Functional Dependences
| Autor: | L. A. Pomortsev, V. I. Tsurkov |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
0209 industrial biotechnology
Sequence Computer Networks and Communications Computer science Relational database Applied Mathematics 010102 general mathematics 02 engineering and technology Disjoint sets Term (logic) Mathematical proof 01 natural sciences Theoretical Computer Science Set (abstract data type) Algebra 020901 industrial engineering & automation Control and Systems Engineering Embedding Computer Vision and Pattern Recognition 0101 mathematics Partially ordered set Software Information Systems |
| Zdroj: | Journal of Computer and Systems Sciences International. 59:957-980 |
| ISSN: | 1555-6530 1064-2307 |
| Popis: | As all computational programs, derivation sequences of functional dependences are twice partially ordered sets: by following the instructions in the program and by their execution in time. Order consistency is achieved by the theoretical multiple embedding of one into another. Hereinafter, such sets are referred to as cascade ordered, and there is no need to resort to the terminology of the relational database theory for them. It is possible to represent the derivation sequence in the form of a special union of almost disjoint simple subsequences referred to as pointed sets here. It is achieved by applying a gluing operation $$\ae $$ to them. The process of forming a cascade-ordered set of pointed sets is reflected in the title by the term Synthesis. This paper is aimed at studying this process. The final section of the paper sets forth the principles of Analysis, i.e., decomposition of a specified cascade-ordered set into so-called AR cones. This issue will be completely resolved in subsequent papers. Here, logic schemes that are designed to calculate predicates from the given ones are applied for proofs. Flowcharts that are common to algorithmization are less frequently used. Their combined application serves the purposes of automating mathematical proofs. The logical toolkit of the paper is a prerequisite for constructing a mathematical model of artificial intelligence. |
| Databáze: | OpenAIRE |
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