Testability Properties of Divergent Trees

The testability of a class of regular circuits called divergent trees is investigated under a functional fault model. Divergent trees include such practical circuits as decoders and demultiplexers. We prove that uncontrolled divergent trees are testable with a fixed number of test patterns (C-testable) if and only if the module function is surjective. Testable controlled trees are also surjective but require sensitizing vectors for error propagation. We derive the conditions for testing controlled divergent trees with a test set whose size is proportional to the number of levels p found in the tree (L-testability). By viewing a tree as overlapping arrays of various types, we also derive conditions for a controlled divergent tree to be C-testable. Typical decoders/demultiplexers are shown to only partially satisfy Land C-testability conditions but a design modification that ensures L-testability is demonstrated.