Data based algorithmic algebra
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DATA BASED ALGORITHMIC ALGEBRA UDC 519.681
V. G. Akulovskiy
Abstract. A system of algorithmic algebras is formed on the basis a modified Glushkov computer model. Data are formalized and specified at inputs and outputs of D-operators and, hence, the formal apparatus constructed is based on data. Some properties of D-operators and operations that form the signature of the algebras are proved and the possibility of construction of derived D-operators is shown. Keywords: computer model, algebra of algorithms, data, algorithmic construction, operation of algebra of algorithms, D-operator. INTRODUCTION The most important and often determining role of data in developing algorithms and programs has been gradually comprehended by the programming community. As a result, the following two approaches to programming were sequentially formed: control-based programming and data-based programming. The fundamental difference between them is that, in the first case, the creation of an algorithm (program) is based on the development of control structures and, in the second case, it is based on the development of data structures. Embodiments of these approaches became the paradigms of structural and object-oriented programming. At the present time, these two approaches and, accordingly, these two programming paradigms exist rather independently and, moreover, compete among themselves. It seems obvious that there is a sufficiently wide class of software systems whose development allow for ambiguous choices of some approach (paradigm). This is apparently explained by the fact that each of approaches is not universal but is oriented towards development of its own (sufficiently wide) class of software systems and does completely correspond to the specificity of systems of other classes. Moreover, well-known technologies within the framework of which the mentioned programming paradigms are implemented are not sufficiently formalized in the overwhelming majority of cases despite all their advantages. Hence, the problem of development and formalization of the third (intermediate) approach allowing one to combine properties of the other two approaches seems to be topical. In this case, the well-known formal apparatus oriented towards the development of algorithms is the system of algorithmic algebras (SAA) [1] (which is being modified and developed [2, 3]) within the framework of which both mentioned programming paradigms are implemented. However, the potential of the computer model underlying the mentioned formal apparatus is not completely used. This statement is confirmed by [4] which asserts that Glushkov’s computer model can be treated differently (under some additional assumptions). Developing this idea, the author asserts that a modification of the mentioned computer model allows one to construct an algebraic apparatus with some prescribed properties. Proceeding from this assertion, we will construct an apparatus involving means for the description of algorithms in a form that would provide the possibility of a simultaneous and consi
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