519.87 Structural theory of complex systems. Model synthesis

Brodsky Y. I. (ФИЦ ИУ РАН)

COMPLEX SYSTEMS, STRUCTURAL THEORY, MODEL SYNTHESIS, GEOMETRIC THEORY OF BEHAVIOR, MODEL-ORIENTED PROGRAMMING, FORMALIZATION OF SOCIAL SCIENCES


doi: 10.18698/2309-3684-2022-3-98123


The purpose of this work is to organize from a unified viewpoint the results of the author's work in the field of the structural theory of complex systems modeling and the practice of their implementing of the last two decades. We propose a formal definition of the complex system computer model, as a species of structure in the sense of N. Bourbaki — the М (System) species of structure, based on the humanitarian analysis of the complex systems key properties, recognized by a number of authoritative researchers and practicians in this field, and the assumption of the possibility of constructing a mathematical computer model of a complex system, — the closure hypothesis. The class of mathematical objects defined by the М species of structure has the following two properties: a complex created by combining a finite number of mathematical objects of the М species of structure, according to the certain rules, is itself a mathematical object of the same М species of structure. The computation organization process is same for all the mathematical objects of the М species of structure and therefore can be implemented by a single universal program for the simulation calculations organization. The presence of these two properties of the М species of structure representatives allows us to build an end-to-end technology for the description, synthesis and software implementation of the complex systems models — Model Synthesis and Model-Oriented Programming. By studying the morphisms of the М species of structure base sets of the model constructed with the model synthesis help, and the invariants limiting such morphisms, we obtain a formal mathematical language for the study of complex open (changing their composition) systems. By conducting a traditional humanitarian discourse, one can always correlate it with the corresponding object of the М species of structure — translating the higher-level language of humanitarian concepts into mathematical language. The proposed theory has a practical application in the field of development, description and implementation of complex software systems. A new programming paradigm is proposed — Model-Oriented Programming, which is a complete implementation of CAD methods in programming. When developing a software system, it is possible to stay within the framework of declarative programming, avoiding imperative, which greatly simplifies both its development and implementation, and subsequent debugging.


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