The diversity and heterogeneity of real-world systems makes it impossible to naturally model them only with existing modeling languages. For this reason, models are often constructed using domain specific modeling languages as metamodels, which must themselves be specified by metametamodels. In this paper we present a new approach, based on the category theory, to specify metamodels. A grammar for modeling processes (PN, CSP, EPC, etc.) syntactically defines processes and then presents a set of reaction rules that model the behavior of the system. We will see that the categorical sketch is sufficiently expressive to be able to support the constructions needed to visually define the syntax of a graphical modeling language. The category theory also provides appropriate structures to model the behavioral rules of a real system.
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.
The current objectives to increase the standards of quality and efficiency in manufacturing processes can be achieved only through the best combination of inputs, independent of spatial distance between them. This paper proposes modelling production processes based on membrane structures introduced in [4]. Inspired from biochemistry, membrane computation [4] is based on the concept of membrane represented in its formalism by the mathematical concept of multiset. The manufacturing process is the evolution of a super cell system from its initial state according to the given actions of aggregation. In this paper we consider that the atomic production unit of the process is the action. The actions and the resources on which the actions are produced, are distributed in a virtual network of companies working together. The destination of the output resources is specified by corresponding output events.
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