On the complexity of the design synthesis problem

In this paper we present and analyze a formal model of a design process, emphasizing the synthesis part. The design artifact description is identified as an algebraic structure. The desired function and constraints are mapped to the artifact description using an evolutionary process that can be visualized as a feedback loop of analysis, synthesis and evaluation. A special case of the synthesis activity, called the Basic Synthesis Problem (BSP), is addressed. The BSP is shown to be NP-Complete. As a consequence, tractability can be obtained by enforcing constraints on the artifact structure. As such, we present a model having an element of descriptive design theory that is also a framework for the future development of computational support systems and automatic design tools.