Synthesis System Оf Algebra Algorithms Formulas

2021;
: pp. 11 - 22
Authors:
1
Lviv Polytechnic National University
2
Lviv Polytechnic National University

In the article the authors have developed a mathematical support for the process of generating subject unitherms of formulas of algebra of algorithms. The analysis of features of construction of formulas of algebra of algorithms as a result of which it was found out, that today, subsystems with realization of processes of generation of subject unitherms on the basis of abstract unitherms with the subsequent adaptation of formulas are not realized in known systems that served as stimulus to intellectual analysis formulas of algebra of algorithms. It is described that the synthesis of algebra formulas of algorithms, and especially the generation of subject unitherms on the basis of abstract ones is an extremely complex and laborious process. Since all elements of the formula are interconnected, all changes in the algorithm’s formula affect its structure. Therefore, this is the main reason for the complexity of the described processes. One aspect of the synthesis of the formulas of the algebra of algorithms is the process of generating subject unitherms based on abstract unitherms. The signs of operations of the algebra of algorithms are briefly described. Mathematical support of the process of synthesis of algorithm algebra formulas is developed, which takes into account vertical and horizontal orientation and type of algorithm algebra formula: text unitherm, sequencing operation, elimination operation, parallel operation and corresponding cyclic sequencing operations, elimination and parallelization, as well as geometric parameters. The process of generating subject unitherms on the basis of abstract ones is previously described. The list of necessary eliminations and sequences for the synthesis of the corresponding formulas is determined. According to the properties of the signs of operations of the algebra of algorithms, the synthesized formulas of the algorithms are minimized by the number of unitherms. Also, in accordance with the properties of the formulas of the algorithms of algebra, the corresponding unitherms are taken out as signs of operations, as a result of which the formula of the algorithm for the synthesis of algorithm formulas is obtained taking into account the generation of subject unitherms based on abstract unitherms.