Presentation of Mathematical Induction by Formula of Algebra of Algorithms

The analysis of the axiom of mathematical induction, which is given by the formula of mathematical logics is presented in the paper. It has been established that the famous formula of mathematical induction is executed only in case of ordered values of the variable linked by a quantifier. This ordering is not described analytically. Algebra of algorithms is applied for an analytical description of ordering of the variable values. The axiom of mathematical induction is described by the formula of algebra of algorithms

Models of Identification of Sequencing Operation

We have described two developed models of identification of the sequencing operation of the modified algebra of algorithms. One of them is the analytical one, and the second is a diagram of sequences. We have applied the modified algebra of algorithms to create an analytical model. The model in a shape of a diagram of sequences was built on the basis of the program code in Microsoft Visual Studio .Net. Models describe the identification of the sequencing operation with horizontal and vertical orientation. Also, the operators of the operations of sequencing are identified by the models

Synthesis and optimization of sequencing operation algorithm

Synthesis and optimization ways of sequencing operation applied in computer system, are described in the paper. The ways are general, and use sequencing and eliminating operations of algorithm algebra. They allow for automated synthesis of the sequencing operations. Optimization of algorithm formulas has been made on the basis of the properties of sequencing operations

Models of a Computer System with an Abstract Graphic Element

A general model of a computer system with an abstract graphic element and a model of formation of an element form have been designed using the means of algebra of algorithms, the system of algorithmic algebras and platforms

An algebraic model of the subsystem for the computer generation of elimination operation

A brief analysis of the known methods of non-algebraic and algebraic descriptions of algorithms has been presented. The features of the elimination operation being a term of the algorithm algebra have been shown. An algebraic model of the computer generation of the elimination operation has been synthesized by means of the algorithm algebra. The model has been implemented with the help of software on the platform Microsoft Visual Studio.NET. The models of subsystem as a graph and a diagram of sequences have been designed as well