Transformational Design of Digital Systems Related to Graph Rewriting

Abstract. For high-level synthesis transformational design is a promising design methodology which combines correctness by construction and interactive design. In this design methodology the design steps are behaviour preserving transformations of one design representation into another. Because of the importance of visualisation of design-information several kinds of graphs are used as design representations. Transformational design based on graph representation is closely related to rewriting of (sub)graphs. In this paper the formal aspects of transformational design are related to graph rewriting theory. It is shown how a formal framework for transformational design can benefit from graph rewriting theory. Especially preconditions for the application of transformation rules can be based on generally formulated preconditions from graph rewriting theory. Moreover a general graph concept unifies graph representations and a formal framework for transformational design based on this general graphs and their rewriting unifies several transformational design approaches based on different graph representations. Unfortunately semantical aspects, the behaviour preserving aspects, which are of great importance for transformational design are not a part of graph rewriting theory. A consistent embedding of these behaviour preserving aspects in the formal framework based on graph rewriting is defined and presented in this paper. The discussion of formal aspects is accompanied by an informal discussion.