Special Year in Computational Complexity Theory

计算复杂性理论特别年

• 批准号: 9987077
• 负责人: Avi Wigderson
• 金额: $ 30万
• 依托单位: Institute For Advanced Study
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-09-01 至 2001-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9987077&HistoricalAwards=false
• 关键词: Special; Year; Computational; Complexity; Theory

Avi Wigderson9987077This project will support three senior researchers to participate in a special year on computational complexity theory at the Institute for Advanced Studies. These researchers will attract the participation of other top researchers in computational complexity. Computational complexity theory has opened up one of the most exciting fields of scientific and mathematical research over the last 20 years, with dramatic achievements and fundamental understandings appearing at a high rate. One obvious explanation for the recent progress in this field is that this research is guided by a few clear and focused questions, deeply motivated on scientific, practical and philosophical grounds. The most central of these are:P=NP?, or more generally, are the many natural computational problems we can't solve really difficult?NP=coNP?, or more generally, what constitutes a difficult theorem to prove:P=BPP?, or more generally, does randomization really help efficient computation?BPP=QP?, or more generally, can quantum mechanics be efficiently simulated classically?Resolving any of these questions is clearly very long term goal, but each has stimulated the development of concepts, problems, proof techniques and results which start paving a path towards a possible resolution.But what really characterized the progress, and explained much of the successes so far, was the unveiling of many rich and beautiful connections between the sets of concepts and sub-problems each of these major questions gave rise to. There is little doubt that such connections are, and will be, the foundation for understanding the major questions of complexity theory. Indeed, these connections are what is making the complex world of computational complexity into a theory. The focus of this special year at the Institute will be to better understand these connections and their implications, to unify and extend them, and to look for new ones.

Avi Wigderson9987077该项目将支持三名高级研究人员参加高级研究所计算复杂性理论的特殊年。 这些研究人员将吸引其他计算复杂性领域顶尖研究人员的参与。计算复杂性理论开辟了过去 20 年来最令人兴奋的科学和数学研究领域之一，取得了巨大的成就和基础性的理解。 对于这一领域最近取得的进展，一个明显的解释是，这项研究是以一些明确而有针对性的问题为指导的，深深地基于科学、实践和哲学基础。 其中最核心的是：P=NP？，或者更一般地说，我们无法解决的许多自然计算问题真的很困难吗？NP=coNP？，或者更一般地说，什么构成了一个难以证明的定理：P=BPP ？或者更一般地说，随机化真的有助于高效计算吗？BPP=QP？或者更一般地说，量子力学可以有效地进行经典模拟吗？解决这些问题中的任何一个显然都是非常长期的目标，但每个问题都刺激了概念的发展、问题、证明技术以及开始为可能的解决方案铺平道路的结果。但是，真正体现这一进展的特征，并解释了迄今为止的大部分成功，是揭示了这些主要概念和子问题之间的许多丰富而美丽的联系。引发了疑问。 毫无疑问，这种联系现在是、将来也将是理解复杂性理论主要问题的基础。 事实上，这些联系使计算复杂性的复杂世界成为一种理论。 该研究所这一特殊年份的重点将是更好地理解这些联系及其影响，统一和扩展它们，并寻找新的联系。