Probabilistic construction and manipulation of Free Boolean Diagrams

We propose a data structure for Boolean functions termed the Free Boolean Diagram (FBD). We extend a previous result to show that the equivalence of two Free Boolean Diagrams can be decided probabilistically in polynomial time. Based on the equivalence checking method, we develop a set of algorithms for the probabilistic construction of Free Boolean Diagrams from multilevel combinational logic circuits, and for their manipulation. These algorithms are modified versions of ordered Binary Decision Diagram manipulation methods. We provide the implementation details of a Free Boolean Diagram package. Results on applying this package to problems in combinational logic verification are presented.