Redundancy identification using transitive closure

We analyze all signals of a combinational circuit simultaneously for redundancy. The state of a signal is represented by two binary variables. The first variable is the logic value of the signal. The second variable is the observability status of the signal with respect to all primary outputs. Boolean equations specify local relationships of these variables in a manner similar to the neural network or Boolean satisfiability method. All pairwise terms appearing in these Boolean equations are used to construct an implication graph, for which the transitive closure graph is obtained. Any signal assignments or relations found from the transitive closure are substituted into higher-order terms of the Boolean equations, some of which reduce to pairwise terms. Such cases are iteratively included in the transitive closure until no more reductions are possible. In the final transitive closure, all signals are examined for the following conditions of redundancy: (1) If a signal and its complement imply each other (contradiction) then both stuck-at faults on that signal are redundant; (2) If one value implies the other value (fixation) then one of the stuck-at faults on that signal is redundant; (3) If the true observability status of a signal implies its own false observability status, then both stuck-at faults of that signal are redundant; (4) If a certain value of a signal implies the false observability status, then the corresponding stuck-at fault is redundant. We give ISCAS '85 benchmark results. For c6288, we could identify 31 out of 33 redundancies. The percentage of identified redundancies was not always that high, but the algorithm has polynomial complexity and we discuss its limitations.