Polynomial Formal Veri cation of Multipliers

Until recently, verifying multipliers with formal methods was not feasible, even for small input word sizes. About two years ago, a new data structure, called Multiplicative Binary Moment Diagram (*BMD), was introduced for representing arithmetic functions over Boolean variables. Based on this new data structure, methods were proposed by which veriication of multipliers with input word sizes of up to 256 Bits is now feasible. Only experimental data has been provided for these veriication methods until now. In this paper, we give a formal proof that logic veriication with *BMDs is polynomially bounded in both, space and time, when applied to the class of Wallace-tree like multipliers.