An Abstract Model of Behavior for Hardware Descriptions

As part of our research on the Carnegie-Mellon University Design Automation System, we have been investigating methods for proving that the system produces correct designs from correct specifications. We have developed a mathematical model for the behavior of hardware descriptions, which we have used to prove that some of the optimizing transformations used in the design system preserve behavioral equivalence. The model, which is based on regular expressions modified by predicates to show data dependence, goes beyond the usual computational models used in program verification, in that it takes into account the proper sequencing of those "events" which represent interactions with the environment. This paper presents the model, shows how it can be used to represent the behavior of descriptions in an ISP-like hardware description language, and gives an example proof of a transformation.