My purpose in this lecture is to explain how the representation of algorithms by recursive programs can be used in complexity theory, especially in the derivation of lower bounds for worst-case time complexity, which apply to all—or, at least, a very large class of—algorithms. It may be argued that recursive programs are not a new computational paradigm, since their manifestation as Herbrand-Goedel-Kleene systems was present at the very beginning of the modern theory of computability, in 1934. But they have been dissed as tools for complexity analysis, and part of my mission here is to rehabilitate them. I will draw my examples primarily from van den Dries' and the joint work in [3,2], incidentally providing some publicity for the fine results in those papers. Some of these results are stated in Section 3; before that, I will set the stage in Sections 1 and 2, and in the last Section 4 of this abstract I will outline very briefly some conclusions about recursion and complexity which I believe that they support.
展开▼
机译：我在本演讲中的目的是解释如何在复杂性理论中使用递归程序的算法表示形式，尤其是在推导最坏情况下的时间复杂性的下限时，该下限适用于所有（或至少非常大的）类的算法。可以说递归程序并不是一个新的计算范式，因为它的表现形式是Herbrand-Goedel-Kleene系统，它是在1934年现代可计算性理论的开始出现的。但是，它们已不被用作复杂性分析的工具。 ，而我在这里的任务之一就是修复它们。我将主要从范登德斯（van den Dries）和[3,2]中的联合著作中借鉴我的例子，顺便提一下这些论文的出色结果。其中的一些结果在第3节中进行了说明。在此之前，我将在第1部分和第2部分中作好准备，在本摘要的最后第4部分中，我将非常简要地概述一些有关递归和复杂性的结论，我相信它们是支持的。
展开▼
