Evaluation of Binary Decision Diagrams Complexity Using Relative Arithmetic Width

Many logic synthesis methods are based on the optimization of reduced-order binary decision diagrams (BDDs). The complexity of a BDD greatly depends on the chosen order of variables. Most of the methods find optimal variable ordering focused primarily on some subset of BDD parameters, for example, the size, the number of paths, the average path length, etc. In some cases, there is a need for using several parameters for the evaluation of overall BDD complexity. Therefore, this article proposes a BDD complexity evaluation using the relative arithmetic width (RAW) parameter. This parameter is calculated as the arithmetic mean of the BDD relative widths over all its levels. The RAW expresses the numerical value of the relative shape of the BDD. Experimental results with optimal variable ordering demonstrate the efficiency of the approach.