A Categorical Model of Process Co-Simulation

Abstract

A set of dynamic systems in which some entities undergo transformations, or receive certain services in successive phases, can be modeled by processes. The specification of a process consists of a description of the properties of this process as a mathematical object in a suitable modeling language. The language chosen for specifying a process should facilitate the writing of this specification in a very clear and simple form. This raises the need for the use of various types of formalisms that are faithful to the component subsystems of such a system and which are capable of mimicking their varied dynamics. Often in practice, the development of domain specific languages is used to provide building blocks adapted to the processes. Thus, the concept of multi-paradigm modeling arises which involves the combination of different types of models, the decomposition and composition of heterogeneous specified models as well as their simulation. Multi-paradigm modeling presents a variety of challenges such as coupling and transforming the models described in various formalisms, the relationship between models at different levels of abstraction, and the creation of metamodels to facilitate the rapid development of varied formalisms for model specification. The simulation can be seen as a set of state variables that evolve over time. Co-simulation is a synthesis of all simulations of the components of the system, coordinated and synchronized based on interactions between them. The theory of categories provides a framework for organizing and structuring formal systems in which heterogeneous information can be transferred, thus allowing for the building of rigorous cohesion bridges between heterogeneous components. This paper proposes a new model of co-simulation of processes based on the category theory.

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