Automatic Correction of Arithmetic Circuits in the Presence of Multiple Bugs by Groebner Basis Modification

Abstract

One promising approach to verify large arithmetic circuits is making use of Symbolic Computer Algebra (SCA), where the circuit and the specification are translated to a set of polynomials, and the verification is performed by the ideal membership testing. Here, the main problem is the monomial explosion for buggy arithmetic circuits, which makes obtaining the word-level remainder become unfeasible. So, automatic correction of such circuits remains a significant challenge. Our proposed correction method partitions the circuit based on primary output bits and modifies the related Groebner basis based on the given suspicious gates, which makes it independent of the word-level remainder. We have applied our method to various signed and unsigned multipliers, with various sizes and numbers of suspicious and buggy gates. The results show that the proposed method corrects the bugs without area overhead. Moreover, it is able to correct the buggy circuit on average 51.9× and 45.72× faster in comparison with the state-of-the-art correction techniques, having single and multiple bugs, respectively.