Computation models and algebra of algorithms

Abstract

An analysis of the existing, intuitive computation models is presented, that is the virtual machines of Turing, Post, Kolmogorov, Schönhage, Aho-Ullman-Hopcroft as well as the algorithms of Markov and Krinitski, and the recursive functions. The need for tools of precise, mathematical formulation and possible transformation of the algorithms is indicated. Consequently, an algebra of algorithms is defined using the axiomatic method. The algebra is based on the operations of sequencing, elimination, paralleling and inverting as well as cyclic sequencing, cyclic elimination and cyclic paralleling, all of them performed on the so-called uniterms.