PolyCleaner: clean your polynomials before backward rewriting to verify million-gate multipliers

Nowadays, a variety of multipliers are used in different computationally intensive industrial applications. Most of these multipliers are highly parallelized and structurally complex. Therefore, the existing formal verification techniques fail to verify them. In recent years, formal multiplier verification based on Symbolic Computer Algebra (SCA) has shown superior results in comparison to all other existing proof techniques. However, for non-trivial architectures still a monomial explosion can be observed. A common understanding is that this is caused by redundant monomials also known as vanishing monomials. While several approaches have been proposed to overcome the explosion, the problem itself is still not fully understood. In this paper we present a new theory for the origin of vanishing monomials and how they can be handled to prevent the explosion during backward rewriting. We implement our new approach as the SCA-verifier PolyCleaner. The experimental results show the efficiency of our proposed method in verification of non-trivial million-gate multipliers.