Computability and Incomputability

The conventional wisdom presented in most computability books and historical papers is that there were several researchers in the early 1930’s working on various precise definitions and demonstrations of a function specified by a finite procedure and that they should all share approximately equal credit. This is incorrect. It was Turing alone who achieved the characterization, in the opinion of G¨odel. We also explore Turing’s oracle machine and its analogous properties in analysis.

• Type: Conference
• Year: 2007
• Where: CIE
• Authors: Robert I. Soare
• Keywords: CIE 2007, Conventional Wisdom, Turing’s Oracle Machine, Various Precise Definitions