Processor Verification Using Efficient Reductions of the Logic of Uninterpreted Functions to Propositional Logic

TL;DR

This paper introduces an efficient method for processor verification by reducing the logic of uninterpreted functions to propositional logic, enabling faster analysis with Boolean tools.

Contribution

It presents a novel reduction technique exploiting formula properties to simplify verification conditions, improving efficiency in processor correctness proofs.

Findings

Significant reduction in verification time for pipelined processors

Effective exploitation of positive equations in formulas

Demonstrated improvements over existing methods

Abstract

The logic of equality with uninterpreted functions (EUF) provides a means of abstracting the manipulation of data by a processor when verifying the correctness of its control logic. By reducing formulas in this logic to propositional formulas, we can apply Boolean methods such as Ordered Binary Decision Diagrams (BDDs) and Boolean satisfiability checkers to perform the verification. We can exploit characteristics of the formulas describing the verification conditions to greatly simplify the propositional formulas generated. In particular, we exploit the property that many equations appear only in positive form. We can therefore reduce the set of interpretations of the function symbols that must be considered to prove that a formula is universally valid to those that are ``maximally diverse.'' We present experimental results demonstrating the efficiency of this approach when verifying pipelined processors using the method proposed by Burch and Dill.