Computability Theory and its Applications

可计算性理论及其应用

• 批准号: 312501-2013
• 负责人: Csima, Barbara
• 金额: $ 1.09万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=548769
• 关键词: Computability; Theory; its; Applications

Up to the mid 19th century or so, mathematics was mostly algorithmic. Proofs of existence were usually done by giving an actual construction of the object. As mathematics began to become more abstract, people began to study the notions of algorithms and computability. The first stumbling block was on the definition of what it meant to be algorithmic or computable. When faced with an algorithm, people would agree that it was one, but how would one show that something could not be computed, or solved by an algorithm? By the 1930s, work of Turing and others culminated in an acceptable notion of computability.

直到19世纪中叶左右，数学主要是算法。存在的证据通常是通过给物体的实际结构来完成的。随着数学开始变得越来越抽象，人们开始研究算法和计算性的概念。第一个绊脚石是关于算法或可计算的含义的定义。当面对算法时，人们会同意这是一种，但是如何表明无法通过算法来计算或解决某些问题？到1930年代，图灵（Turing）和其他工作的工作最终达到了可接受的可计算性概念。