By Marshall C. Yovits
Includes long evaluation articles on desktop aided good judgment synthesis for VLSI chips, sensor-driven clever robotics, complex thoughts in dealing with dispensed facts, info stream and keep watch over among people and pcs and automatic balloting.
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As our computational experience shows, the quality of the designed networks is better than those designed by known heuristic logicdesign methods, especially for large networks. For example, a network with 25 gates for 3 output functions that was designed by a heuristic method in Su and Nam (1971) was improved by the transduction method into a network of 15 gates. The method yields networks with an absolutely minimal number of gates for the majority of functions tested when the networks require 10 or fewer gates, where the integer-programming logic-design method can be applied for examining the minimality of networks with 10 or fewer gates.
But the design of minimal networks with more than 10 gates is too time-consuming, as illustrated in Fig. 9. 1: Outline of the transduction method Step 1. Design an initial NOR network by any known design method. Or, any network to be simplified can be used as an initial network. 32 SABURO MUROGA Step 2. Remove redundant part of the network, by the use of permissible functions. ) Step 3. Perform network transformation (which is local or global), using permissible functions. Step 4 . Repeat Steps 2 and 3, until no further improvement is possible.
3 Computational Results of Minimal Networks The implicit-enumeration method can be used to solve our integerprogramming problem. The computer programs ILLIP and ILLIP-2 were developed based on the implicit-enumeration method. The numbers of the variables and the inequalities in the integer-programming formulation of logic design of a minimal NOR gate network are very large. But the number of nonzero coefficients is not large and the majority of these nonzero coefficients are + 1 and -1. Therefore, the storage requirement of these nonzero coefficients is much smaller and the computation with them is much faster than it appears.