Testability properties of BDDs

This paper discusses the relationship among BDDs (binary decision diagrams), unateness and redundancy. We show that redundancy is introduced in logic circuits when the general case (binate) of the Shannon decomposition is used for unate functions. As ROBDDs are not able to specify in their structure if a decomposition in a node or a group of nodes is unate, circuits derived from ROBDDs will contain redundancies. We also show that, in order to represent unateness using BDD structures, it is necessary to use BDDs in which variables are not ordered and read more than once. Based on these observations, we propose a new algorithm that is able to generate robustly-path-delay-testable circuits without increasing the delay, by removing redundancies directly on the BDD representation.