Bourbaki’s structure theory in the problem of complex systems simulation models synthesis and model-oriented programming

Brodsky, Yury I.

doi:10.1134/s0965542515010054

Cited by 9 publications

(10 citation statements)

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“…To solve this problem completely, the works [4,5] proposed the concepts of Model Synthesis and Model-Oriented Programming. The central point of these concepts is a construction of universal agent for agent simulation -so called "model-component".…”

Section: From Model Synthesis To the Geometric Theorymentioning

confidence: 99%

“…The execution of one or another method-element depends on the situations arising in the system j E , to which the process is able to respond, they will be called the set of its methods-events. Typical characterizations (3), (4) shows, from where the methods-elements and methods-events are taken, (5) - (7) shows what characteristics of the model are transmitted to methods-elements and accepted from them, typical characterization (8) sets the rules for switching elements under the influence of the events. Axioms 1 R -8 R complement and clarify the typical characterizations (1) - (8).…”

Section: Model-component Species Of Structurementioning

confidence: 99%

“…Such a description makes it quite simple to prove in the language of the set theory that combining a finite number of models-components into a modelcomplex gives to it the same structure. Therefore, a model-complex is itself a model-component [4]. This is one of two principal features of the modelscomponents family.…”

Section: Model-component Species Of Structurementioning

confidence: 99%

“…This way we act all the time of modeling, regardless of the type of model, its size, subject area, etc. More details on this can be found in [4,5]. Now we can tell in details, how the axiom of the behavior of the model-component 11 R works:…”

Section: Model-component Species Of Structurementioning

confidence: 99%

“… Combining a finite number of family representatives into a complex according to certain rules [4], does not take the resulting construction beyond the family.…”

Section: Model-component Species Of Structurementioning

confidence: 99%

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Elements of Geometric Theory of Complex Systems Behavior

Brodsky

2020

Wseas Transactions on Systems and Control

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The paper proposes the elements of a geometric theory of behavior. The basis of this theory is Model Synthesis - an end-to-end technology for describing, synthesizing and implementing agent models. Its main achievement – is the formalization of an agent by a mathematical object - a species of structure in the sense of N. Bourbaki. Algorithms that implement actions of agents are included in the base sets of this species of structure. Let us consider morphisms of the base sets with the special attention to the actions mappings. It occurs that unrestricted mappings of base sets can radically change system’s behavior. We can use invariants as restrictions of mappings, if demand their preservation under admissible morphisms. As a result, we can obtain a classification of the systems behavior depending on the invariants that persist during the mappings.

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Section: From Model Synthesis To the Geometric Theorymentioning

confidence: 99%

Section: Model-component Species Of Structurementioning

confidence: 99%

Section: Model-component Species Of Structurementioning

confidence: 99%

Section: Model-component Species Of Structurementioning

confidence: 99%

“… Combining a finite number of family representatives into a complex according to certain rules [4], does not take the resulting construction beyond the family.…”

Section: Model-component Species Of Structurementioning

confidence: 99%

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Elements of Geometric Theory of Complex Systems Behavior

Brodsky

2020

Wseas Transactions on Systems and Control

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Sustainable Development of Social Systems: a View from the Geometric Theory of Behavior

Brodsky

2021

IFAC-PapersOnLine

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Structural theory as a research language for open complex systems, including social ones

Brodsky

2023

E3S Web of Conf.

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The application of structural theory allows to see the same universal construction, called a “model,” applicable to a broad class of modeling areas. Everything in the world is a model in this theory: an agent, a complex of agents, and a complex of complexes. We can say that the widely known formula: “One in all and all in One” is true in this area, as well as the well-known aphorism of H. Poincare: “Mathematics is the art of calling different things by the same name.” The application of geometric theory is the consideration of morphisms of base sets and the assigning invariants that allow a complex system to remain under such morphisms. The proposed language for the complex systems behavior makes it possible to draw several interesting conclusions about the nature of complex open systems, simply due to its means of distinguishing entities. A complex system must sacrifice a part of its power (the most expensive and liquid that it has) to preserve its laws of life (maintain its structure and set of axioms). Otherwise, it will not be able to remain itself. It is interesting to remember that many religions teach that this world stands on the sacrifice.

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Bourbaki’s structure theory in the problem of complex systems simulation models synthesis and model-oriented programming

Cited by 9 publications

References 0 publications

Elements of Geometric Theory of Complex Systems Behavior

Elements of Geometric Theory of Complex Systems Behavior

Sustainable Development of Social Systems: a View from the Geometric Theory of Behavior

Structural theory as a research language for open complex systems, including social ones

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