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理论计算机科学专题:概率可检查证明

Topics In Theoretical Computer Science: Probabilistically Checkable Proofs
课程网址: https://ocw.mit.edu/courses/18-408-topics-in-theoretical-computer...  
主讲教师: Prof. Dor Minzer
开课单位: 麻省理工学院
开课时间: 2022-01-01
课程语种: 英语
中文简介:
在本课程中,我们将介绍概率可检查证明(PCP)的理论,并证明它的一些基本后果以及最近的进展。更具体地说,课程的前半部分将专门讨论基本PCP定理的(代数)证明以及与近似问题的基本关系。然后,我们将继续讨论更高级的主题,例如硬度放大、长代码框架、唯一博弈猜想及其含义以及 2 比 2 博弈定理。
课程简介: In this course, we will present the theory of Probabilistically Checkable Proofs (PCPs), and prove some fundamental consequences of it as well as more recent advances. More specifically, the first half of the course will be devoted to the (algebraic) proof of the basic PCP Theorem and basic relation to approximation problems. We will then move on to more advanced topics, such as hardness amplification, the long-code framework, the Unique-Games Conjecture and its implications, and the 2-to-2 Games Theorem.Show less    
关 键 词: 概率可检查证明; 基本后果; 长代码框架
课程来源: 麻省理工学院公开课
数据采集: 2024-02-05:chenjy
最后编审: 2024-02-05:chenjy
阅读次数: 9