Rozszerzenie algebry algorytmów

W artykule za pomocą metody aksjomatycznej przedstawiono pod-stawy rozszerzonej algebry algorytmów. Algebra ta obejmuje operacje sekwencjonowania, eliminowania, zrównoleglenia, rewersowania oraz cyklicznego sekwencjonowania, eliminowania i zrównoleglenia, wykonywane na unitermach. Podano definicję algorytmu, do jakiego ma zastosowanie rozszerzona algebra algorytmów. Istotę zdefiniowanych operacji rozszerzonej algebry algorytmów zilustrowano za pomocą rysunków. Na przykładzie pokazano jej zastosowanie. Opis porównano z opisem algorytmów, otrzymywanym za pomocą klasycznej algebry algorytmów.

Very often algorithms are described verbally or like a unit - diagram. The well known methods offering algorithms are: Post [1], Turing [2], Aho-Ullman-Hopcroft [3] or Schönhage [4] virtual machines, recursive functions (calculus λ, Church) [5], Markov algorithms [6], b-complexes of Kolmogorov (Kolmogorov machine) [7], Krinitski universal algorithms [8], and algorithm algebra [9]. It is obvious that verbal methods, and methods of unit - diagram, as well as, algorithm methods [1] - [8] are depicted by the intuition, not formally. Only by means of the algorithm algebra, the algorithm description is getting into the formulae form, on abstract and meaningful levels. The transformation and investigation of their trustworthiness can be made on formulae of algorithms with minimization target, by the specific operations. These advantages of algebra algorithms beyond other methods of algorithm description make a ground for it's using. Classical algorithm algebra [9] manipulates over conditional uniterms, which are delivered only two meanings (e.g. "yes" and "no" or "0" and "1").Very often conditional uniterm can deliver more than two meanings. For example, automation systems are operated in a plenty of regimes. Score parameters are controlled in checking systems. It is possible to describe the algorithms which contain more than 2 conditions by means of classical algebra algorithms. These formulae - algorithms are complicated for apprehension. To avoid possible mistakes, the expansion of the algorithm algebra is presented in the paper.