Geodesic
Hygiene of derivation sequences
Nečetkie sistemy i mâgkie vyčisleniâ, Tome 16 (2021) no. 1, pp. 34-57.

Voir la notice de l'article provenant de la source Math-Net.Ru

The Sequence of Derivation (DS) of the of Functional Dependence from the set of other FD is the program of the notional Computer which is operated by commands F and B. Formalization of DS presents her as the Cascade Ordered Set (COS) with Orders of consecution $\leqslant^{0)} :=\mathbf{=\twoheadrightarrow}$ and of conclusion $\leqslant^{1)} :=\mathbf{=\Rrightarrow}$ inheriting undesirable properties of programming from DS: 1. Variability of software development; 2. The uncontrollable outgoing nesting (branching); 3. A possibility of repetition in the program of functionally equivalent fragments; 4. Other. This work is aimed at eradication of these shortcomings of DS that is reached by rectificaition of algorithms and is implemented by the chain of Lemma 3 $\mapsto$ Theorem 4 $\mapsto$ Theorem 4 which eventually will allow each DS put in correspond the algebraic expression functionally equivalent to it in some D-algebra.
Keywords: syllogism, analysis, synthesis, database table, relation, attribute, scheme, key of table, functional dependence, graph, logical scheme, cortege, projection, nesting, D-algebra, PO, POS, RDB, TRDB. 
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L. A. Pomortsev; V. I. Tsurkov. Hygiene of derivation sequences. Nečetkie sistemy i mâgkie vyčisleniâ, Tome 16 (2021) no. 1, pp. 34-57. http://geodesic.mathdoc.fr/item/FSSC_2021_16_1_a2/

[1] Dejt K. D., Introduction to Database Systems, Izdatelskij dom Vilyams, M., SPb., 2001 (in Russian) | MR

[2] Emelichev V. A., Melnikov O. I., Sarvanov V. I., Tyshkevich R. I., Lectures on Graph Theory, Nauka Publ., Moscow, 1990 (in Russian) | MR

[3] Kleene S. C., Introduction To Metamathematics, Wolters-Noordhoff Publishing, Amsterdam, 1957

[4] Kon P., Universal algebra, Mir Publ., Moscow, 1968 (in Russian) | MR

[5] Kurosh A. G., Lectures on general algebra, Fizmatlit Publ., Moscow, 1962 (in Russian)

[6] Mejer D., The theory of relational databases, Mir Publ., Moscow, 1987 (in Russian)

[7] Pomortsev L. A., “Calculation of moments of ordinal statistics of consecutive sums of symmetrically dependent random variables”, Proceedings of the Moscow Mathematical Society, 46 (1983), 201–242 (in Russian) | MR | Zbl

[8] Pomortsev L. A., “Combinatorial-symmetric analysis of multidimensional random walks”, Discrete mathematics, 3:1 (1991), 21–41 (in Russian) | MR | Zbl

[9] Pomortsev L. A., “Algebraic interpretation of the completeness of the axioms of inference”, Fundamental and Applied Mathematics, 8:1 (2002), 195–219 (in Russian) | MR | Zbl

[10] Pomortsev L. A., “Functional dependency algebras in relational database theory”, Proceedings of the Institute of System Analysis of the Russian Academy of Sciences. Dynamics of inhomogeneous systems, 29:1 (2007), 169–183 (in Russian)

[11] Pomortsev L. A., Tsurkov V. I., “Algebraization of inferring functional dependences in relational databases”, Journal of Computer and Systems Sciences International, 58:2 (2019), 212–228 | DOI | DOI | Zbl

[12] Pomortsev L. A., Tsurkov V. I., “SYNTHESIS AND ANALYSIS OF sequences of output of functional dependencies of tables”, Journal of Computer and Systems Sciences International, 6 (2020), 152–176 | Zbl

[13] Pomortsev L. A., Tsurkov V. I., “Order alteration in a cascade-ordered set”, Fuzzy Systems and Soft Computing, 15:2 (2020), 96–115 (in Russian) | DOI

[14] Ulman D., Databases in Pascal, Mashinostroyeniye Publ., Moscow, 1990 (in Russian)

[15] Yablonskij S. V., Introduction to Discrete Mathematics, Nauka Publ., Moscow, 1986 (in Russian) | MR

[16] Codd E. F., “A relational model for large shared data banks”, Communications of the ACM, 13 (1970), 377–387 | DOI | Zbl

[17] Codd E. F., “Extending the database relational model to capture more meaning”, ACM Transactions on Database Systems, 1979, no. 4, 397–434 | DOI

[18] Szpilrajn E., “Sur l'extension de l'ordre partiel”, Fundamenta Mathematicae, 16 (1930), 386–389 | DOI | Zbl