On the Rectifiability of Arithmetic Circuits using Craig Interpolants in Finite Fields

Abstract

When formal verification of arithmetic circuits identifies the presence of a bug in the design, the task of rectification needs to be performed to correct the function implemented by the circuit so that it matches the given specification. This paper addresses the problem of rectification of buggy finite field arithmetic circuits. The problems are formulated by means of a set of polynomials (ideals) and solutions are proposed using concepts from computational algebraic geometry. Single-fix rectification is addressed – i.e. the case where any (set of) bugs can be rectified at a single net (gate output). We determine if single-fix rectification is possible at a particular location, formulated as the Weak Nullstellensatz test. Subsequently, we introduce the concept of Craig interpolants in polynomial algebra over finite fields and show that the rectification function can be computed using algebraic interpolants. Experimental results demonstrate the superiority of our approach against SAT-based approaches.