Tags:Arithmetic Circuits, Computer algebra and Formal verification

Abstract:

The paper describes a practical, commercial-strength software tool for the verification of integer arithmetic circuits. It covers different types of adders, multipliers, fused add-multiply circuits, and some dividers - the circuits whose computation can be represented as a polynomial. The verification uses an algebraic model of the circuit and is accomplished by rewriting the polynomial of the binary encoding of the primary outputs (output signature), using the polynomial models of the logic gates, into a polynomial over the primary inputs (input signature). The resulting polynomial provides the arithmetic function of the circuit and hence can be used to extract its functional specification from the gate-level implementation. The rewriting uses an efficient \textit{And-Inverter Graph} (AIG) representation to enable extraction of the essential arithmetic components of the circuit. The tool is integrated with the popular ABC system. Its efficiency is illustrated with impressive results for large integer multipliers, fuse-multiply circuits, and divide by constant circuits. The entire verification system is offered in an open source ABC environment together with an extensive set of benchmarks.

Rewriting Environment for Arithmetic Circuit Verification