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Mathematical Formalization and Abstract Description
Abstract
The chapter is dedicated to the possibilities of formalization of an investigated object and its abstract description with appropriate mathematical means. At the beginning, the need to decompose complex systems is discussed to facilitate the following model study. The appropriate elements of a standard formal theory, applied in mathematical formalization and the abstract description of the investigated object, are formulated. A major place is devoted to the application of discrete and stochastic structures for the formalization of computer systems and processes for the purposes of further modeling. In the part of discrete means, the possibilities of formalization based on set theory, binary and weighted graphs, theory of finite automata are discussed. Some examples of specific applications are also given. The discussion of stochastic means is mainly focused on the application of elements of probability theory (random processes, streams of random events), the theory of Markov processes (in particular the application of Markov chains), and the theory of queues.
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