Edge Valued Binary Decision Diagrams

Abstract

In this paper we present a new data structure called Edge-Valued Binary-Decision Diagrams (evbdd). An evbdd is a directed acyclic graph, that provides a canonical and compact representation of functions that involve both Boolean and integer quantities. In general, evbdds p r o vide a more versatile and powerful representation that Ordinary Binary Decision Diagrams. We rst describe the structure and properties of evbdds, and present a general algorithm for performing a variety of binary operations. Next, we describe an important extension of evbdds, called Structural evbdds, and show h o w t h e y c a n b e u s e d for hierarchical veri cation.

Representations of Elementary Functions Using Edge-Valued MDDs

“…EVBDDs form a subset of K*BMDs [5] and factored EVBDDs (FEVBDDs) [19] that allow additive and multiplicative edge weights. Thus, K*BMDs and FEVBDDs also represent elementary functions compactly.…”

Spectral Interpretation and Applications of Decision Diagrams

“…The methods should be computationally more effective as Vilenkin-Chrestenson functions do not possess the half spectrum property. [38,46,102]. The use of nodes with greater number of outgoing edges [77] permitted extension of DDs representations to MV [49,50,86], and other discrete functions on notnecessarily Abelian groups [88].…”

“…In a similar way, the spectral transforms for switching functions can be calculated over Edgevalued DDs [45], and their generalizations [46,102]. Through Multiple-Place DDs [82] and their integer-valued counterparts, DDs based calculation methods can be extended to spectral transforms for MV and complex-valued functions on any finite, not necessarily Abelian group [49,97], and other related algebraic structures [98].…”

Decision diagrams for discrete functions: classification and unified interpretation

“…Factored Edge-Valued Binary DDs (FEVBDDs) are a generalization of EVBDDs by permitting additive and multiplicative weights at the edges [50]. Both additive and multiplicative w eights at the edges connecting nonterminal nodes are determined as combinations of partial arithmetic transform coecients.…”