工作范畴理论家的理论计算机科学
Theoretical Computer Science for the Working Category Theorist
摘要:
理论计算机科学讨论有关计算的基础问题。它提出并回答诸如“什么是计算?什么是可计算的?什么是有效可计算的?”、“什么是信息?”、“什么是随机?“、“什么是算法?我们将用范畴论的基本语言提出许多主要的主题和定理。令人惊讶的是,理论计算机科学中许多有趣的定理和概念都是函子性和复合性的简单结果,只要你找到正确的范畴和连接它们的函子。
英文摘要:
Theoretical computer science discusses foundational issues about computations. It asks and answers questions such as "What is a computation?", "What is computable?", "What is efficiently computable?","What is information?", "What is random?", "What is an algorithm?", etc. We will present many of the major themes and theorems with the basic language of category theory. Surprisingly, many interesting theorems and concepts of theoretical computer science are easy consequences of functoriality and composition when you look at the right categories and functors connecting them.
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