On a procedural platform for the theory of algorithms - Zubenko, Vitaly (PHYSICO-MATHEMATICAL MODELLING AND INFORMATIONAL TECHNOLOGIES, 2023)
The work is devoted to an attempt to mathematically clarify the general concept of an algorithm. It is proposed to move away from the practice existing in the theory of algorithms to define a specific representative class of algorithms and associate the general concept of an algorithm with it. Our approach is based on the idea of mathematically specifying a more abstract and broader concept - a computational procedure[2], and then in narrowing it down to the notion of an algorithm. The concept of operational table of procedures is introduced, and the basis of narrowing is the solvability of these tables. The place of basic mathematical models of algorithms and calculations within the proposed procedural platform, such as finite automata, Turing machines, normal algorithms, discrete Glushkov transforms, formal grammars, Post systems, and others, is considered. As it turns out, procedures with finite operational tables correspond to almost all of these models. Issues of arrangement and systematization of all currently existing models of algorithms and calculus within the framework of this platform are discussed.