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The research methodology of mathematical support of computer-aided design systems has been formulated based on the algebra of algorithms and the mathematical induction. The methodology has been illustrated on the example of the research of the known but slightly complicated Euclidean algorithm.
A comparative analysis of algebraic methods of mathematical models synthesis of complex computer systems and information technologies has been done. A model of an abstract subsystem has been synthesized by means of algebra of algorithms and the system of algorithmic algebras.
The mathematical models of diagrams of using cases of computer systems and information technologies (for Microsoft Visual Studio.NET platform) are built in the forms of Glushkov's algorithmic algebra systems, Zeitlin-Pogorilyi's modified algorithmic algebra systems, modified algorithmic algebras and primitive program algebras (PPA), which is an example of programing algebra class of composite type...
We consider the use of the modified algebra of algorithms to formalize the grammars and derivations of context-free grammars. The inference rules and the derivations themselves of several applied grammars have been given by formulas of modified algebra of algorithms. We illustrate the use of operations of sequencing as well as operations of paralleling to describe the inference rules.
We consider the use of the modified algebra of algorithms to formalize the grammars and outputs of context-free grammars. The inference rules and the derivations themselves of several applied grammars have been given in formulas of modified algebra of algorithms. We illustrate the use of operations of sequencing as well as operations of paralleling to describe the rules of output.
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