Augmented sifting of multiple-valued decision diagrams

Discrete functions are now commonly represented by binary (BDD) and multiple-valued (MDD) decision diagrams. Sifting is an effective heuristic technique which applies adjacent variable interchanges to find a good variable ordering to reduce the size of a BDD or MDD. Linear sifting is an extension of BDD sifting where XOR operations involving adjacent variable pairs augment adjacent variable interchange leading to further reduction in the node count. In this paper, we consider the extension of this approach to MDDs. In particular, we show that the XOR operation of linear sifting can be extended to a variety of operations. We term the resulting approach augmented sifting. Experimental results are presented showing sifting and augmented sifting can be quite effective in reducing the size of MDDs for certain types of functions.