AF: Large: Theory of Computation - Pushing the State-of-the-Art

AF：大：计算理论 - 推动最先进的技术

• 批准号: 1412958
• 负责人: Avi Wigderson
• 金额: $ 200万
• 依托单位: Institute For Advanced Study
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-09-01 至 2020-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1412958&HistoricalAwards=false
• 关键词: AF; Large; Theory; Computation; Pushing

This project is aimed at understanding a variety of fundamental questions in the theory of computation. It will be carried out via the postdoctoral mentoring program at the Institute for Advanced Study, and as such the specific topics of focus will evolve with the postdocs present each year. Current foci include, among others, the following:- The power of formulas. Formulas is the most basic mathematical and computational descriptive mechanisms. Understanding their minimal length for natural problems captures at once limitation on the space requirements, as well as the potential parallelism inherent in the problem. The award will focus on the most challenging direction, which has so far resisted attack - proving limitation of formulas. More generally, the researchers will pursue proving limitations of other natural computational models, especially arithmetic computation.- The power of relaxationsThe "meta-algorithms": Linear and semi-definite relaxations of integer programs, are among the most fruitful and powerful techniques for solving (or finding approximate solutions) to optimization problems. The award will focus on understanding the limits of these techniques. This work ties in naturally to understanding the limitations of natural proof systems and of natural strategies for search algorithms.- Peeking inside the "black-box"One of the most useful paradigms in programming and learning is the encapsulation of objects as black-boxes, to which only input-output access is allowed. With this utility come limitations which can hopefully overcome if we are allowed some access into the internal workings of the black box. Modeling such access, in scientific experiments, machine learning and computational complexity is a challenge the researchers plan to pursue.Computational complexity, a foundational core of computer science, has proved itself a remarkably deep and fruitful fountain of problems, ideas and techniques over the past decades. The research agenda is expected to be a driver of innovation in Theoretical Computer Science and related disciplines. Some of the areas of study have potential implications outside theory, especially machine learning, coding theory, scientific discovery and more. On the educational side, the mentoring program furthers the quality of IAS postdocs to serve as outstanding teachers, graduate advisors and academic leaders and innovators in one of the most exciting branches of science today. Whether IAS alumni pursue a career in academia or industry their impact on technology and on the training of new generations undergraduate and graduate education is immense.

这个项目旨在理解计算理论中的各种基本问题。它将通过高等研究院的博士后指导计划进行，因此，每年的具体重点主题将随着博士后的出现而变化。目前的重点包括：-公式的力量。公式是最基本的数学和计算描述机制。对于自然问题，理解它们的最小长度可以立即捕获对空间需求的限制，以及问题中固有的潜在并行性。该奖项将侧重于迄今为止最具挑战性的方向，即证明公式的局限性。更一般地说，研究人员将寻求证明其他自然计算模型的局限性，特别是算术计算。-松弛的力量“元算法”：整数程序的线性和半确定松弛，是解决（或寻找近似解）优化问题的最有效和最强大的技术之一。该奖项将侧重于理解这些技术的局限性。这项工作与理解自然证明系统和搜索算法的自然策略的局限性自然相关。在编程和学习中最有用的范例之一是将对象封装为黑盒，只允许输入-输出访问。有了这个实用程序，如果允许我们进入黑匣子的内部工作，就有可能克服这些限制。在科学实验、机器学习和计算复杂性中对这种访问进行建模是研究人员计划追求的挑战。计算复杂性是计算机科学的基础核心，在过去的几十年里，它已经证明了自己是一个非常深刻和富有成果的问题、思想和技术的源泉。该研究议程有望成为理论计算机科学和相关学科创新的驱动力。一些研究领域在理论之外有潜在的影响，特别是机器学习、编码理论、科学发现等等。在教育方面，指导计划进一步提高了IAS博士后的质量，使他们成为当今最令人兴奋的科学分支之一的杰出教师、研究生顾问、学术领袖和创新者。无论IAS校友是在学术界还是工业界从事职业，他们对技术以及对新一代本科和研究生教育培训的影响都是巨大的。

项目成果

Automating cutting planes is NP-hard

自动化切割平面是 NP 困难的

• DOI: 10.1145/3357713.3384248
• 发表时间: 2020
• 期刊: STOC 2020: Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing
• 作者: Göös, M;Koroth, S;Mertz, I;Pitassi, T.
• 通讯作者: Pitassi, T.

Search problems in algebraic complexity, GCT, and hardness of generator for invariant rings

不变环生成元的代数复杂性、GCT 和硬度搜索问题

• 发表时间: 2020
• 期刊: Computational Complexity Conference (CCC
• 作者: Garg, A;Ikenmeyer, C;Makam, V;Oliveira, R;Walter, M;Wigderson, A.
• 通讯作者: Wigderson, A.

AND testing and robust judgement aggregation

AND 测试和稳健的判断聚合

• DOI: 10.1145/3357713.3384254
• 发表时间: 2020
• 期刊: STOC 2020: Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing
• 作者: Filmus, Y;Lifshitz, N;Minzer, D;Mossel, E.
• 通讯作者: Mossel, E.

Geometric rank of tensors and subrank of matrix multiplication

张量的几何秩和矩阵乘法的子秩

• 发表时间: 2020
• 期刊: Electronic colloquium on computational complexity
• 作者: Kopparty, S;Moshkovitz, G;Zuiddam, J.
• 通讯作者: Zuiddam, J.