Efficient Equivalence Checking of Nonlinear Analog Circuits using Gradient Ascent

In this paper, we present an optimized methodology for performing state-space-based equivalence checking of nonlinear analog circuits by using a gradient-ascent-based search algorithm to efficiently traverse a common state space. Essentially, the method searches for critical regions where the functional behaviors of two circuit designs show the greatest divergence. The key challenges in this approach are the mapping of both designs onto a common canonical state space, the computation of the gradient, and the exclusion of unreachable regions within the state space. To address the first challenge, we use locally linearized systems and leverage the Kronecker Canonical Form (KCF). To facilitate the computation of the gradient, we employ a purpose-built target function, and to exclude unreachable regions, we utilize vector projection techniques. Through experiments with nonlinear analog circuits and a scalability analysis, we demonstrate the successful and efficient computation performed with the proposed methodology, achieving speedups of up to 468 times.