Symbolic Computer Algebra for Multipliers Revisited - It's All About Orders and Phases

Using Symbolic Computer Algebra (SCA) enabled a huge progress in formal verification of arithmetic circuits in recent years. Several different approaches have been proposed showing great success especially for the verification of multipliers. Some of them are based on precomputing and simplifying polynomials for specific circuit structures like converging cones while others take advantage of known or detected hierarchy information to replace and simplify particular sub-circuits of the design. In this paper we propose a new method that avoids the use of such methods and applies only two dynamic approaches: (1) choosing a good substitution order for the backward rewriting process and (2) adjusting the phases of signals occurring in the intermediate polynomials during the verification process. Both methods are simply based on a greedy local search taking the sizes of intermediate polynomials into account. Our experimental results show that this method is very competitive with already existing tools and it improves their robustness, e.g. against optimizations of the verified circuits using logic synthesis.