LSAT-An Algorithm for the Synthesis of Two Level Threshold Gate Networks

In the second set of problems, we compared the performance of the described algorithm with the performance of a popular two-level minimizer, ESPRESSO [4]. To allow for a fair comparison, LSAT was constrained to use only and gates in the rst level and or gates in the second level. A detailed description of the functions used for these tests can be found in [8]. The input data sets were created by randomly generating a minterm and getting its correct classication from the function description. For each function, 2 dierent inputs were tried, with a number of minterms of 200 and 600. According to the generation procedure, all instances of the problem should accept a solution with no more cubes than the theoretical minimum. Table 2 shows that although no specic code optimization was performed for the special case when a cube cover is to be found, the performance of the algorithm still compares well with a classic two-level optimizer. In particular, it obtains results that are either similar or better than ESPRESSO and much faster. Moreover, the speed gain increases with the size of the problem. This is due, in part, to the fact that LSAT does not require an explicit cover for the f DC set while ESPRESSO does. Is is also clear from these results that both programs obtain results very far from the minimum in a large number of cases. A dierent approach to this optimization problem may lead to better results in these and other problems. 5 Conclusions and future work We designed and implemented and algorithm for the synthesis of threshold gate networks and have shown, experimentally, that results near the theoretical minimum are obtainable in many problems. The algorithm has a run time polynomial in the input size and its performance degrades slowly with the size of the problem. Experimental results have also pointed out the need for a deeper understanding of this particular version of this optimization problem. In particular , the reason why, in some cases, dierent algorithms nd similar solutions very far from the optimum requires further study. The most interesting single direction for future work in this area is the extension of these techniques to the synthesis of multi-level networks. Classic multi-level techniques [5] can provide the starting point for such an algorithm. Another interesting research topic related with this work is the design of multi-valued threshold gate networks. committee. …