Online Computability and Differentiation in the Cantor Space.
Lecture Notes in Computer Science(2018)
摘要
This paper investigates a notion of differentiation for functions on the Cantor space. We study the existence and complexity of this derivative, particularly for online and computable online functions. It is shown that a random online function has no derivative at any computable point. It is shown that if a computable online function F has derivate m > 0 at a weakly 1-random point, then F has derivative m on a set of positive measure. We also explore the family of online functions on the Cantor space which represent real-valued functions.
更多查看译文
关键词
Cantor Space, Online Function, Computable Real Functions, Barmpalias, Cenzer
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络