Theorems on Redundancy Identi cation

There is a class of implication-based methods that identify logic redundancy from circuit topology and without any primary input assignment. These methods are less complex than automatic test pattern generation (ATPG) but identify only a subset of all redundancies. This paper provides new results to enlarge this subset. Contributions are a xed-value theorem and two theorems on fanout stem unobservability. Our framework is an implication graph of signal controllabilities and observabilities represented as Boolean variables. Besides the conventional implication edges this graph also contains partial implications implemented by AND nodes. An analysis of the transitive closure (TC) of this graph provides many redundancies. Weaknesses of this procedure are in dealing with the e ects of xed-valued variables on TC and the lack of observability relations across fanouts. The xed-value theorem adds unconditional edges from all variables to the xed variable and then recomputes TC recursively until no new xed nodes are found. The stem unobservability theorems determine the observability status of a fanout stem from its dominator set, which either has xed values or is unobservable. Results are considerably improved from the previously reported implication-based identi ers. In the c5315 circuit we identify 58 out of 59 redundant faults. All 34 redundant faults of c6288 are identi ed. Besides, our procedure can classify faults according to the causes of their redundancy, namely, unexcitable, unobservable, or undrivable. For the future research, we provide examples of cases where the present method still fails.