Formalizing the Representativeness of Verification Models using Morphisms

Abstract

With the increasing complexity that is being introduced to engineered systems, the literature suggests that verification may benefit from theoretical foundations. In practice and in teaching of system engineering (SE), we typically define a verification model (simulation, test article, etc.) under the assumption that the model is a valid representation of the system design. Is this assumption always true? In this article, we explore the use of system theoretic morphisms to mathematically characterize the validity of representativeness between verification models and corresponding system design.

Study of Equivalence in Systems Engineering Within the Frame of Verification

“…Although other theoretical bodies of research exist with potential, Wymorian systems theory has the pieces necessary to address the research question. Specifically, Wymorian systems theory includes theoretical foundations for problem spaces of functions (PSF) (e.g., [40,53]), which are used to characterize system requirements (SR) and aspects of verification requirements referred to as verification requirement problem spaces (VRPS); morphisms (e.g., [53,72]), which are used to characterized equivalence between SR and VRPS as well as between system designs (SD) and verification models (VM); and hierarchy of system specification (e.g., [44]), which is used as a basis to characterize hierarchy of detail from SR and VRPS to varying detail of SD and VM structure.…”

“…Figure 22: High-level metamodel of T3SD [72] T3SD earned its name from the cotyledons that form three spaces of "system designs": the functional space shown as problem space of functions in Figure 1, the buildable space shown as Technology in Figure 1, and implementable space shown as Implementation & Testing (and verification) in Figure 1. Note, a system design in the context of T3SD is a model that exists initially prior to the existence of a final product.…”