Self-similar structure of wire length distribution of random logic

摘要

A general scaling theory is proposed to estimate a wire length distribution based on the self-similarity structure of random logic. It is theoretically shown that the d-dimensional wire length distribution denoted by f(l)(d) is of the form f(l)(d) similar to l(-yl(d)) with a characteristic exponent y(l)(d) = alpha(d) + 2 - dp for l < l(crossover) with some crossover length l(crossover), where l is a wire length and p is the Rent's partition exponent. The parameter alpha(d) is equal to d - 1 and d for serialized and parallel wiring configurations, respectively. For wire lengths larger than l(crossover), f(l)(d) similar to l(-y2(d)) is obtained with y(2)(d) = alpha(d) + 2. These results are in good agreement with experiments. (c) 2005 Elsevier Ltd. All rights reserved.