Modeling Techniques in Design-by-Refinement Methodologies

Embedded system design methodologies that are based on the effective use of multiple levels of abstraction hold promise for substantial productivity gains. Starting the design process at a high level of abstraction improves control over the design and facilitates verification and synthesis. In particular, if we use a rigorous approach to link the levels of abstraction, we can establish properties of lower levels from analysis at higher levels. This process goes by the name of “design by refinement”. To maximize its benefit, design by refinement requires a formal semantic foundation that supports a wide range of levels of abstraction (e.g., from differential equations describing physical behaviors to high-level requirement specifications). We describe such a semantic foundation, and give examples of how it integrates several well-known models for reactive systems. The semantic foundation allows us to establish the relationships among the different levels of abstractions even when non-homogeneous models are used to describe the design. These relationships are essential to establish properties and to document assumptions about the way the models are used, preventing common errors that are difficult to detect and may otherwise require long redesign cycles.