Grouping heuristics for word-level decision diagrams

Word-level decision diagrams (WLDDs), like EVBDDs, *BMDs, HDDs, K*BMDs, are powerful tools in circuit verification. For some arithmetic circuits, like multipliers, formal verification was possible for the first time using WLDDs. Besides a good variable ordering and the decomposition types the size of a WLDD essentially depends on the grouping of the outputs. In this paper we study output grouping in more detail. We give examples showing that an exponential reduction or an exponential blow-up can be obtained dependent on grouping. We describe efficient heuristics for output grouping given a circuit description in the form of a netlist. Experimental results are given to demonstrate the efficiency of our approach.