One main genre of algorithmic derandomization comes from the construction of probability distributions with small support that fool a randomized algorithm. This is especially well-suited to parallelization, i.e. NC algorithms. A significant abstraction of these methods can be formulated in terms of fooling polynomial-space statistical tests computed via finite automata (Sivakumar 2002); this encompasses $k$-wise independence, sums of random variables, and many other properties. We describe new parallel algorithms to fool general finite-state automata with significantly reduced processor complexity. The analysis is also simplified because we can cleanly separate the problem-specific optimizations from the general lattice discrepancy problems at the core of the automaton-fooling construction. We illustrate with improved applications to the Gale-Berlekamp Switching Game and to approximate MAX-CUT via SDP rounding.

翻译：算法去随机化的一个主要流派源于构建具有小支撑集的概率分布来欺骗随机化算法。这种方法特别适合并行化，即NC算法。这些方法的一个重要抽象可以表述为欺骗通过有限自动机计算的多项式空间统计检验（Sivakumar 2002）；这涵盖了$k$阶独立性、随机变量和以及其他许多性质。我们提出了新的并行算法，能以显著降低的处理器复杂度欺骗一般有限状态自动机。分析过程也得到简化，因为我们可以清晰地将问题特定的优化与自动机欺骗构造核心中的一般格点差异问题分离开来。我们通过改进的Gale-Berlekamp开关博弈应用和基于SDP舍入的近似MAX-CUT问题来展示其效果。