Modeling and Integration for Complex Systems

Abstract

In this paper, we propose a way forward in modeling complex software-managed systems that relies on two well-known mathematical constructs, the subdirect product and the quotient by a congruence relation. These mathematical techniques allow us to build models that correspond to different aspects of / concerns about the system (which we call viewpoints), and to integrate them afterwards. It does require models of the interactions among these viewpoints, but that kind of consideration should occur no matter what kind of modeling is being carried out. This provides an explicit way for designers to enumerate and analyze all the design considerations, which, of course, they should be considering anyway, but often do not because there are difficulties in studying model interactions, and no particular theoretical base for doing so. This paper is our first attempt to address that problem. We describe some of the relevant viewpoint models, show how some of their interactions might be modeled, and explain the underlying mathematical methods.