Abstruct-We propose a heuristic for finding minimal costtables for use in the design of multiple-valued logic circuits. It is an iterative approach, in which a good table of size t is composed of a good table of size t -1, etc. We analyze its performance, comparing it with three other heuristics. The importance of finding good cost-tables is demonstrated by an analysis that shows there is a wide variation in both cost-table performance and in the performance of heuristics for generating cost-tables.We study linear cost, a general cost function of which two previously studied cost functions are special cases. It is shown that the minimal cost-table using one of the (infinitely many) linear cost functions is identical to a minimal cost-table using any other linear cost function. Thus, a heuristic for finding the minimal cost-table using the linear cost function is independent of the specific cost function parameters. This result and our observation of well-studied nonlinear cost functions indicate that cost-table design is only marginally dependent on the cost function.We show two additional results on cost-
In the costtable approach to logic design, a function is realized as a combination of functions from a table. The objective of the synthesis is to find the least cost realization, where realization cost is the sum of the costs of the functions used, plus the cost of combining them. The costs of costtable functions are defined by a cost function, which represents chip area, speed, power dissipation, or a combination of these factors. We show that there is an arbitrarily large set S of cost functions all of which yield the same minimal realization from a given costtable. This implies, for example, that every minimal realization of any function over a cost function in S is independent of the actual cost function used. Furthermore, we show that, with any cost function, if the cost of combining functions from a costtable F is sufficiently large, the realizations behave as if the cost function belongs to S. That is, any minimal realization of a functionf, using costtable F, is one of the minimal realizations o f f using F and a cost function in S. Our interpretation of these results is that there are not as many distinct costtables as originally thought.
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