Both non-determinism and multi-level networks can be used to compactly characterize logic structures as well as all the flexibilities allowed for optimizing them. Synthesis results can be improved by allowing the manipulation of a larger class of networks, called ND networks. These are multi-level logic networks which embody both non-determinism and multi-valued signals, and thus enhance compactness and expressiveness. We develop a complete theory for representing and manipulating ND networks. It is shown that an ND network’s behavior can be classified into at least three types, all of which coalesce when the network becomes deterministic. The theory addresses the classical transformations commonly applied to optimize deterministic binary networks, such as node minimization, elimination, and decomposition. These are analyzed with respect to their effects on each type of network behavior, leading to modifications of some operations to make them safe, i.e. guaranteeing that the new behavior remains within the network’s specification. Finally, it is proved that all three types of behaviors can be used in a hierarchical synthesis paradigm. 1
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