基于信息的复杂性简史
A brief history of information-based complexity
摘要：
这篇论文是在2008年6月6日德国耶拿弗里德里希·席勒大学授予亨里克·沃兹尼亚科夫斯基荣誉博士学位之际发表的。基于信息的复杂性（IBC）是对连续问题的算法和计算复杂性的研究。这些问题的例子包括偏微分方程（特别是薛定谔方程）、非常高维的积分、近似、连续优化和路径积分。由于计算机只有关于连续数学问题的部分信息，因此在信息水平上的对手争论常常导致严格的复杂性界限。这可以与离散问题形成对比，在离散问题中，只有复杂性层次不崩溃的假设是可用的。本文讨论了IBC的前身。它报告开始的最佳迭代理论在60年代初，这是出版特劳布的1964年专着。在70年代，Traub和Wozniakowski开始制定IBC的基础，导致了他们1980年的专著。本文接着介绍了IBC的发展现状。
英文摘要：
This paper was presented on the occasion of an honorary doctoral degree for Henryk Wozniakowski at Friedrich Schiller University in Jena, Germany on June 6, 2008. Information-based complexity (IBC) is the study of algorithms and computational complexity of continuous problems. Examples of such problems include partial differential equations (in particular, the Schrodinger equation) very high dimensional integration, approximation, continuous optimization, and path integration. Because the computer has only partial information about the continuous mathematical problem adversary arguments at the information level often lead to tight complexity bounds. This may be contrasted with discrete problems where only conjectures that the complexity hierarchy does not collapse are available. This paper discusses precursors to IBC. It reports on the beginning of optimal iteration theory in the early 60s which was published in Traub's 1964 monograph. In the 70s Traub and Wozniakowski began to formulate the foundations of IBC leading to their 1980 monograph. The paper continues with the development of IBC to the present.
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