A light-weight framework for hardware verification

Abstract.

We have developed a verification framework that combines deductive reasoning, general purpose decision procedures, and domain-specific reasoning. This paper describes this framework and presents a case study in which we verified an SRT divider circuit. Our proof starts with a high-level description of the SRT algorithm on rational numbers. We verified the correctness of the algorithm. With a sequence of five refinement proofs, we established that a transistor-level implementation with timing is a refinement of a high-level specification of the high-level division algorithm.

Our approach is made practical by integrating formal theorem proving techniques with informal domain-specific reasoning. User-defined inference rules provide domain specific decision procedures, while an LCF-style, first-order-logic theorem prover allows results from these procedures to be combined into a complete proof. Including these “semi-formal” rules as hypotheses of the theorems in which they are used preserves the logical validity of the proofs and tracks and documents the use of domain-specific reasoning.