An Algorithm to Dualize a Regular Switching Function
- 1 March 1979
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Computers
- Vol. C-28 (3) , 238-243
- https://doi.org/10.1109/tc.1979.1675324
Abstract
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 Fd= 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.Keywords
This publication has 3 references indexed in Scilit:
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- A guided bibliography to sortingIBM Systems Journal, 1971
- Threshold LogicPublished by University of California Press ,1965