An Algorithm to Dualize a Regular Switching Function

Given a monotone (nondecreasing) switching function F(x1,···,xn), its prime implicants are the minimal infeasible points, i.e., the minimal solutions to F(x) = 1. A monotone F is regular ifany "right shift" of a feasible point is again feasible. The roofs of a regular function F are those prime implicants al ofwhose right shifts are feasible. The set of these roofs completely determines F. An algorithm is presented to compute the roofs of the dual Boolean function F^d= F̄(x̄) This computation is needed, for example, in the synthesis problem ofthreshold logic. The algorithm "scans" all the 2ⁿpoints in lexicographical order, skipping over intervals which are clearly roof-free. The amount of this work is proportional to the number of prime implicants of F. Encouraging computational experience is reported.