用随机布尔公式计算的布尔函数OR如何生成正确的函数
The Boolean Functions Computed by Random Boolean Formulas OR How to Grow the Right Function
摘要：
在它们的许多用途中，增长过程（概率放大）被用于从不可靠的组件构建可靠的网络，并推导出各类函数的复杂性界限。因此，确定这样的过程的初始条件是一个重要的和具有挑战性的问题。在本文中，我们用初始条件刻画了增长过程，并导出了Valiant（1984）等结果成立的条件。首先，我们完全描述了使用线性连接词的增长过程。第二，通过扩展Savicksman（1990）的分析，通过“限制引理”，我们刻画了使用单调连接词的增长过程，并表明我们的技术也适用于使用其他连接词的增长过程。此外，我们还得到了几个增长过程的收敛速度的显式界，包括Savickstrom（1990）研究的增长过程。
英文摘要：
Among their many uses, growth processes (probabilistic amplification), were used for constructing reliable networks from unreliable components, and deriving complexity bounds of various classes of functions. Hence, determining the initial conditions for such processes is an important and challenging problem. In this paper we characterize growth processes by their initial conditions and derive conditions under which results such as Valiant's (1984) hold. First, we completely characterize growth processes that use linear connectives. Second, by extending Savický's (1990) analysis, via ``Restriction Lemmas'', we characterize growth processes that use monotone connectives, and show that our technique is applicable to growth processes that use other connectives as well. Additionally, we obtain explicit bounds on the convergence rates of several growth processes, including the growth process studied by Savický (1990).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
