On Closedness and Test Complexity of Logic Circuits

The concept of closedness of a set of logic functions under stuck-type faults is introduced. All sets of logic functions closed under stuck-type faults are classified. For the sets of logic functions closed under stuck-type faults, the test complexity and the universal test sets are considered. It is shown that for each class of linear functions, OR functions, and AND functions, both the minimum numbers of multiple fault detection tests and multiple fault location tests are exactly n + 1, where n is the number of inputs of the circuits, and that there exists universal test sets with n + 1 tests to detect and locate all multiple faults in such circuits.