Edge Valued Binary Decision Diagrams

We describe a canonical and compact data structure, called Edge Valued Binary Decision Diagrams (EVBDD), for representing and manipulating pseudo Boolean functions (PBF). EVBDDs are particularly useful when both arithmetic and Boolean operations are required. We describe a general algorithm on EVBDDs for performing any binary operation that is closed over the integers. Next, we discuss the relation between the probability expression of a Boolean function and its representation as a pseudo Boolean function. Utilizing this, we present algorithms for computing the probability spectrum and the Reed-Muller spectrum of a Boolean function directly on the EVBDD. Finally, we describe an extension of EVBDDs which associates both an additive and a multiplicative weight with the true edges of the function graph.

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