and Computational Methods

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.

Plato. Dialogi [Dialogues]. Moscow, Mysl Publ., 1986, 607 p.

Ershov Yu.L., Palyutin E.A. Matematicheskaya logika [Mathematical logic]. Moscow, Nauka Publ., 1987, 336 p.

Bohr N. Atomic physics and human knowledge. John Wiley & Sons Publ., 1958, 101 p.

Norden A.P. Ob osnovaniyah geometrii: sbornik klassicheskih rabot po geometrii Lobachevskogo i razvitiyu ee idej [On the foundations of geometry: a collection of classical works on Lobachevsky's geometry and the development of its ideas]. Moscow, Gostekhizdat Publ., 1956, 527 p.

Dorodnicyn A.A. Informatika: predmet i zadachi [Informatics: subject and tasks]. Vestnik AN SSSR [Bulletin of the USSR Academy of Sciences], 1985, № 2, pp. 85–89.

Malinetsky G.G., Korotaev A.V. Problemy matematicheskoj istorii: istoricheskaya rekonstrukciya, prognozirovanie, metodologiya [Problems of mathematical history: historical reconstruction, forecasting, methodology]. Moscow, URSS, 2008, p. 246.

Brodsky Yu.I. Model'nyj sintez i model'no-orientirovannoe programmirovanie[Model synthesis and model-oriented programming]. Moscow, CC of RAS Publ., 2013, 142 p.

Buslenko N.P. Modelirovanie slozhnyh sistem [Modeling of complex systems]. Moscow, Nauka Publ., 1978, 400 p.

Levansky V.A. Modelirovanie v social'no-pravovyh voprosah [Modeling in social and legal issues]. Moscow, Nauka Publ., 1986, 158 p.

Burbaki N. Teoriya mnozhestv [Set theory]. Moscow, Mir Publ., 1965, 456 p.

Karpov V.E., Konkov K.A. Osnovy operacionnyh sistem: kurs lekcij [Fundamentals of operating systems: a course of lectures]. Moscow, Fizmatkniga Publ., 2019, 328 p.

Mac Lane S. Categories for the working mathematician. New York, Springer, 1978, 317 p.

Buskaran E. Teoriya modelej i algebraicheskaya geometriya [Model theory and algebraic geometry]. Moscow, MCNMO Publ., 2008, 280 p.

Danilov N.Yu. O vzaimosvyazi dekompozicionnyh svojstv ischisleniya rodov struktur i teorii kategorij [On the relationship of the decomposition properties of the calculus of genera of structures and category theory]. Modelirovanie, dekompoziciya i optimizaciya slozhnyh dinamicheskih processov [Modeling, decomposition and optimization of complex dynamic processes], 1996, vol. 11, no. 1–2 (11), pp. 49–62.

Kruglov L.V., Brodsky Yu.I. Model-oriented programming. Proceedings of CBU in Natural Sciences and ICT, 2021, vol. 2, pp. 63–67. DOI: 10.12955/pns.v2.154

Cohn A., Maréchal M.A., Tannenbaum D., Zünd C.L. Civic honesty around the globe. Science, vol. 365, iss. 6448, pp. 70–73.

Pavlovsky Yu.N., Smirnova T.G. Vvedenie v geometricheskuyu teoriyu dekompozicii [Introduction to the geometric theory of decomposition]. Moscow, Phasis Publ., 2006, 169 p.

Kron G. Issledovanie slozhnyh sistem po chastyam diakoptika [Investigation of complex systems in parts diacoptics]. Moscow, Nauka Publ., 1972, 542 p.

Brodsky Yu.I. O priblizhennoj dekompozicii modeli-komponenty [On the a pproximate decomposition of the model-components]. Modelirovanie, dekompoziciya i optimizaciya slozhnyh dinamicheskih processov [Modeling, decomposition and optimization of complex dynamic processes], 2014, vol. 29, no. 1 (29), pp. 119–127.

Dimitrienko Y.I., Dimitrienko O.Y. A model of multidimensional deformable continuum for forecasting the dynamics of large scale array of individual data. Mathematical Modeling and Computational Methods, 2016, no. 1, pp. 105–122.

Бродский Ю.И. Структурная теория сложных систем. Модельный синтез. Математическое моделирование и численные методы, 2022, № 3, с. 98–123.

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