Efficient testing of tree circuits

The authors investigate the testing properties of a class of regular circuits known as trees which include parity circuits, multiplexers, and decoders. Viewing a tree as overlapping one-dimensional arrays makes it possible to extend the testing properties of these arrays to trees. The authors give conditions for individually testing the arrays within a tree with a constant number of tests. Under the best conditions when this can be done, the bound on the number of tests required is proportional to the number of leaf modules in the tree. The authors also present necessary and sufficient conditions for C-testing trees, that is, testing trees of arbitrary size with a constant number of tests. More restrictive conditions are also presented that allow trees to be completely C-tested with the minimum number of tests.