Polynomial Formal Verification of Arithmetic Circuits

Abstract

AbstractThe size and the complexity of digital circuits are increasing rapidly. This makes the circuits highly error-prone. As a result, proving the correctness of a circuit is of utmost importance after the design phase. Arithmetic circuits are among the most challenging designs to verify due to their high complexity and big size. In recent years, several formal methods have been proposed to verify arithmetic circuits. However, time and space complexity bounds are still unknown for most of these approaches, resulting in performance unpredictability. In this paper, we clarify the importance of polynomial formal verification for digital designs particularly arithmetic circuits. We also introduce an Arithmetic Logic Unit (ALU) and prove that formal verification of this circuit is possible in polynomial time. Finally, we confirm the correctness of the complexity bounds by experimental results.KeywordsFormal verificationComplexityPolynomialArithmetic circuitsArithmetic logic unitBinary decision diagram