Ordered and shared, linearly-independent, variable-pair decision diagrams

The paper presents a new kind of decision tree: it is based on nonsingular expansions for pairs of variables. Such trees are used to create linearly independent (LI) decision diagrams (LI DDs). There are 840 nonsingular expansions for a pair of variables, so the number of nodes in such (exact) diagrams is never larger than that of trees with single-variable Shannon, positive Davio, and negative Davio expansions. The LI diagrams are a starting point in a synthesis of multilevel AND/OR/EXOR circuits and can potentially achieve better results than the well-known pseudo-Kronecker functional decision diagrams. They also introduce other gates than AND and EXOR to the synthesis process.