On delay-untestable paths and stuck-fault redundancy

We explore non-robust untestability of paths based on redundant stuck-at faults. Such untestability classification is necessary for a path to be ignored in timing verification and delay testing. A recent result states that redundant stuck-at-0 (s-a-0) and stuck-at-1 (s-a-1) faults of a line imply untestability of rising and falling delay faults, respectively, for all paths through that line. We find that this result only establishes robust untestability of paths. Starting with known examples, where a non-robust test can exist for some paths that pass through the site of a redundant stuck-at fault, we examine various classes of stuck-at fault redundancies. We prove that: (1) an unexcitable or undrivable redundant s-a-0 (s-a-1) fault will make all paths through the fault site non-robustly delay-untestable for rising (falling) transition, and (2) an unobservable fault site (causing both s-a-0 and s-a-1 faults to be redundant) can only classify the passing paths as robustly delay-untestable, Finally, we show that two singly-untestable paths, passing through the sites of separate redundant single stuck-at faults, may form a multiply-testable pair of paths provided the two redundant single stuck-at faults have a multi-fault test