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This paper presents a fast and effective computer algebraic method foranalyzing and verifying non-linear integer arithmetic circuits using a novelalgebraic spectral model. It introduces a concept of algebraic spectrum, anumerical form of polynomial expression; it uses the distribution ofcoefficients of the monomials to determine the type of arithmetic functionunder verification. In contrast to previous works, the proof of functionalcorrectness is achieved by computing an algebraic spectrum combined with alocal rewriting of word-level polynomials. The speedup is achieved bypropagating coefficients through the circuit using And-Inverter Graph (AIG)datastructure. The effectiveness of the method is demonstrated with experimentsincluding standard and Booth multipliers, and other synthesized non-lineararithmetic circuits up to 1024 bits containing over 12 million gates.

Spectral Approach to Verifying Non-linear Arithmetic Circuits