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This set is derived from reachability information of partitions that f (x) depends on. Before applying bi-decomposition to the incompletely specified function [ f (x) · u(x), f (x) + u(x)] the algorithm tries to abstract some of the interval variables while keeping it consistent; this eliminates redundant inputs. 3. From a generated set of choices, partition that best improves timing and logic sharing is selected. 2 illustrates bi-decomposition that benefits from logic sharing. The transformation re-uses logic of g1 , which was present in the network but was not in the fanin of f .

1458–1463, 20–24 April 2009 c [2009] IEEE. P. Khatri, K. N. Kravets and A. Mishchenko In general, for a given completely specified Boolean function its bi-decomposition has form f (x) = h(g1 (x1 ), g2 (x2 )) where h is an arbitrary 2-input Boolean function. , non-disjoint) partition of x. The problem of finding good bidecomposition has been studied in [1, 10, 18, 19, 21]. The main contribution of the material in this chapter is symbolic formulation of bi-decomposition for incompletely specified functions.

In the case of P-circuits with intersection, the testable circuit that we obtain contains two MUXs before the inputs of the final OR gate. One is between the outputs of the decomposed parts and the second is after the output of the intersection. The MUXs are used to test the three single blocks of the circuit separately. In the case of P-circuits without intersection, just one MUX (between the outputs of the decomposed parts before the OR gate) is needed. In this case the proof still holds since we can consider a P-circuit without intersection as a special case of a P-circuit with intersection where the intersection is empty.

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Bass Extremes by Steve Bailey, Victor Wooten

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