Special Year in Computational Complexity Theory

该项目将支持3名高级研究人员参加高等研究院计算复杂性理论特别年。这些研究人员将吸引其他计算复杂性领域的顶尖研究人员的参与。在过去的20年里，计算复杂性理论开辟了科学和数学研究中最令人兴奋的领域之一，取得了惊人的成就，并迅速得到了基本的理解。对这一领域最近进展的一个显而易见的解释是，这项研究是由几个清晰而集中的问题指导的，这些问题深深受到科学、实践和哲学基础的推动。其中最核心的是：P=NP？或者更普遍地说，我们无法解决的许多自然计算问题真的很难吗？或者更一般地说，是什么构成了一个难以证明的定理：P=BPP？或者更普遍地说，随机化真的有助于高效计算吗？或者更一般地说，量子力学可以被有效地模拟吗？解决这些问题显然是一个非常长期的目标，但每个问题都刺激了概念、问题、证明技术和结果的发展，开始为可能的解决方案铺平道路。但是，这一进步的真正特点，以及迄今为止许多成功的原因，是揭示了这些主要问题所产生的概念集和子问题之间的许多丰富而美丽的联系。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，正是这些联系将计算复杂性的复杂世界变成了一个理论。在这个特殊的年份，研究所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。

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.