Computability theory | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-25

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Computability_theory


00:00:58 1 Computable and uncomputable sets
00:04:12 2 Turing computability
00:06:54 3 Areas of research
00:07:23 3.1 Relative computability and the Turing degrees
00:12:59 3.2 Other reducibilities
00:15:34 3.3 Rice's theorem and the arithmetical hierarchy
00:15:52 3.4 Reverse mathematics
00:16:55 3.5 Numberings
00:17:04 3.6 The priority method
00:17:46 3.7 The lattice of recursively enumerable sets
00:17:55 3.8 Automorphism problems
00:18:43 3.9 Kolmogorov complexity
00:20:29 3.10 Frequency computation
00:21:51 3.11 Inductive inference
00:23:34 3.12 Generalizations of Turing computability
00:24:48 3.13 Continuous computability theory
00:25:03 4 Relationships between definability, proof and computability
00:25:33 5 Name
00:25:43 6 Professional organizations
00:26:43 7 See also
00:28:04 8 Notes
00:28:38 9 References
00:30:44 10 External links
00:32:41 Professional organizations
00:33:09 See also



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SUMMARY
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Computability theory, also known as recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definability. In these areas, recursion theory overlaps with proof theory and effective descriptive set theory.
Basic questions addressed by recursion theory include:

What does it mean for a function on the natural numbers to be computable?
How can noncomputable functions be classified into a hierarchy based on their level of noncomputability?Although there is considerable overlap in terms of knowledge and methods, mathematical recursion theorists study the theory of relative computability, reducibility notions, and degree structures; those in the computer science field focus on the theory of subrecursive hierarchies, formal methods, and formal languages.