Algebra algorytmów w przykładach

Artykuł zawiera opis podstawowych operacji algebraicznych jakie można stosować w algorytmice. Przedstawiono kilka prostych przykładów ilustrujących możliwości i aplikacje tematyki. Każda operacja została odzwierciedlona w języku C, bądź została porównana z odpowiadającym jej schematem blokowym.

Algebra of algorithms is a form of mathematical description of an algorithm. The algorithm described in form of formulas can be subjected to algebraic operations and transformations. Properties of these operations are defined in an axiomatic way. The mathematic description of the algorithm is simple, intuitive, and allows to subsequent automatic generation of program code. The main advantage of such approach is possibility to analyze the algorithm at any level of nesting. Some functions (blocks) the algorithm can be treated as uniterms, thus one can look into what happens inside them. A description of basic algebraic operations that can be applied in the study of algorithm operations is presented in the paper. It has been quoted two of the most elementary examples in order to better acquaint with the subject. Each operation is reflected in the C language, and is compared with the corresponding block diagram. Langton algorithm is analyzed as well as the function approximation algorithm for finding the 3-rd order polynomial. These algorithms are described and presented in the form of block diagrams as well as using formulas of algebra algorithms.