Algebraic models of computing machines

Research on the construction and analysis of models of digital computing machines has been developed in recent times mainly in two directions. The basis of the first direction is the method proposed by Glushkov of processing discrete information from the point of view of the theory of automata. The second direction is connected with the work of Lyapunov, Ershov, Glebov and other mathematicians. In this work mathematical models of computing machines are regarded from the standpoint of general algebra. Bordering on this there are also several papers devoted to various ways of formalizing the concept of a computer programme (these questions are dealt with in detail in the survey by Ershov and Lyapunov [26]).
The present survey (without claiming to be exhaustive) is concerned with ways of constructing and studying algebraic-automatic and algebraic models of computing machines. The main attention is given to methods of constructing corresponding models. In conclusion the authors describe one way of modifying an algebraic model, taking into account some elements of the structure of the machine and questions of the operation of a programme inserted in its memory.
We assume that the reader is familiar with some of the basic concepts of general algebra (semigroup, isomorphism, partially ordered set, etc.). This information can be found, for example, in the book of Kurosh [35].