I.O. Slieptsov1

1 LCC "JurInfoR" (Moscow, Russia)

1 igor.slieptsov@mail.com

Systems of two interacting components, one of which is a free actor and the other manages an interaction scenario by dynamically defining a set of possible actions that the actor is able to perform, are widely spread and include the cases of an object interacting with its environment, a client interacting with a server through API, a human interacting with a program and so on. A developer of one of such systems needs tools to design architecture and to debug an implementation. A method aimed at implementation a process of interaction with a language of natural concepts of the domain is wanted.

The goals of the article is 1) to define a class of the systems of interest, 2) to build a model of discrete deterministic interaction of object and its environment, using a language of the category theory, 3) study the model with categorical methods.

A category of interaction processes is defined, it is a formal model of the interaction of interest. An object of the category is a process of interaction, a morphism is a map preserving a structure of a record of particular interaction an object committed. Isomorphisms and monomorphisms are shown to correspond a concepts of equivalent processes and a subprocess, respectively. A category is shown to be finitely complete, that is, it has terminal object, Cartesian product and all finite limits. An initial object (empty process) is also constructed.

The proposed model can be used to implement subsystems that behave like environments. Since categorical approach is expected to be «natural» by providing commutativity and uniqueness in the most of the concepts, the model is more stable to implementation errors and thus is more suitable during debugging.

Slieptsov I.O. Categorical model of discrete deterministic process interaction of an object and an environment. Information-measuring and Control Systems. 2024. V. 22. № 5. P. 46−55. DOI: https://doi.org/10.18127/j20700814-202405-06 (in Russian)

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