No abstract

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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The problem of complex multi-component system processing arises in many fields of science and engineering. A system can be described in terms of its components, behavior, and interaction. This work proposes a new declarative Turing complete “model-oriented” programming paradigm based on the concept of “model-component” - a complex structure with well-defined characteristics and behavior, and no external methods. The set of model-components is closed under the union operation of model-components into “model-complex”. The proposed approach allows the program to describe the complex system and behavior of its components in a declarative way, possesses a higher level of encapsulation than the object-oriented paradigm, involves a reduced amount of imperative programming, and is naturally focused on parallel computations.