Spectral approach to verifying non-linear arithmetic circuits

Abstract

This paper presents a fast and effective computer algebraic method for analyzing and verifying non-linear integer arithmetic circuits using a novel algebraic spectral model. It introduces a concept of algebraic spectrum, a numerical form of polynomial expression; it uses the distribution of coefficients of the monomials to determine the type of arithmetic function under verification. In contrast to previous works, the proof of functional correctness is achieved by computing an algebraic spectrum combined with local rewriting of word-level polynomials. The speedup is achieved by propagating coefficients through the circuit using And-Inverter Graph (AIG) datastructure. The effectiveness of the method is demonstrated with experiments including standard and Booth multipliers, and other synthesized non-linear arithmetic circuits up to 1024 bits containing over 12 million gates.

Rewriting Environment for Arithmetic Circuit Verification

“…To apply ARTi to Booth-encoded multipliers, such as radix-4 Booth multiplier, the design needs to be first preprocessed by extracting the adder trees using the XOR-MAJ extraction approach, described in Section 3, using a command &atree. In addition, a semi-canonical spectral approach that represents the arithmetic functions in an algebraic spectrum form can be used to further improve the ARTi for Booth multipliers [22]. The examples of such circuits, verified with this method, are included in our repository 4 .…”