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命题证明复杂性

Propositional Proof Complexity
课程网址: https://videolectures.net/8ecm2021_razborov_proof_complexity/  
主讲教师: Alexander Razborov
开课单位: 8ECM会议
开课时间: 2021-07-06
课程语种: 英语
中文简介:
命题证明复杂性研究在各种证明系统中,在各种“效率”概念下,可以用无量词形式表示的陈述的有效可证明性。感兴趣的陈述来自各种来源,除了传统的组合原理和其他数学定理外,还包括组合优化、实用SAT求解和运筹学等领域。尽管现代证明复杂性中考虑的许多证明系统仍然是传统的,从希尔伯特风格和基于逻辑的意义上讲,近年来,人们对代数和半代数推理(包括初等凸几何)的系统建模给予了相当多的关注。在这次演讲中,我将试图传达这个充满活力的领域的一些基本思想,包括一个必要的示例示例。
课程简介: Propositional proof complexity studies efficient provability of statements that can be expressed in quantifier-free form, in various proof systems and under various notions of “efficiency”. Statements of interest come from a variety of sources that, besides traditional combinatorial principles and other mathematical theorems, include areas like combinatorial optimization, practical SAT solving and operation research. While many proof systems considered in the modern proof complexity are still traditional, in the sense that they are Hilbert-style and logic-based, a considerable amount of attention has been in recent years paid to systems modelling algebraic and semi-algebraic reasoning, including elementary convex geometry. In this talk I will attempt to convey some basic ideas underlying this vibrant area, including a necessarily based sample of illustrating examples.
关 键 词: 命题证明; 无量词表示; 组合原理
课程来源: 视频讲座网
数据采集: 2024-05-28:liyq
最后编审: 2024-05-28:liyq
阅读次数: 4