随机布尔电路的并行复杂度
Parallel Complexity of Random Boolean Circuits
摘要：
前馈布尔电路的随机实例进行了研究分析和数值。评估这些电路被认为是一个P-完全问题，因此，在最坏的情况下，被认为是不可能执行的，即使是一个大规模并行计算机，在时间上远远小于电路的深度。尽管如此，它被发现，对于一些合奏的随机电路，饱和到一个固定的真值迅速发生，使电路的评估可以在更少的并行时间比电路的深度完成。对于其他合奏饱和不会发生和电路评估显然是困难的。特别地，对于某些由具有五个或更多输入的连接符组成的随机电路，每一级的真实输出的数量是混沌序列。最后，虽然平均情况下的复杂性取决于合奏的选择，它表明，对于所有合奏，它是可以同时构建一个典型的电路连同其解决方案在多对数并行时间。
英文摘要：
Random instances of feedforward Boolean circuits are studied both analytically and numerically. Evaluating these circuits is known to be a P-complete problem and thus, in the worst case, believed to be impossible to perform, even given a massively parallel computer, in time much less than the depth of the circuit. Nonetheless, it is found that for some ensembles of random circuits, saturation to a fixed truth value occurs rapidly so that evaluation of the circuit can be accomplished in much less parallel time than the depth of the circuit. For other ensembles saturation does not occur and circuit evaluation is apparently hard. In particular, for some random circuits composed of connectives with five or more inputs, the number of true outputs at each level is a chaotic sequence. Finally, while the average case complexity depends on the choice of ensemble, it is shown that for all ensembles it is possible to simultaneously construct a typical circuit together with its solution in polylogarithmic parallel time.
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