Turing's halting theorem | Wikipedia audio article
Channel: wikipedia tts
Date: 31/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Halting_problem


00:01:06 1 Background
00:02:55 1.1 Programming consequences
00:04:02 1.2 Common pitfalls
00:07:07 2 History
00:07:41 2.1 Timeline
00:13:38 3 Formalization
00:14:55 3.1 Representation as a set
00:16:08 3.2 Proof concept
00:17:45 3.3 Sketch of proof
00:20:24 4 Computability theory
00:21:57 4.1 Gödel's incompleteness theorems
00:22:12 5 Generalization
00:22:26 5.1 Halting on all inputs
00:22:36 5.2 Recognizing partial solutions
00:22:54 5.3 Oracle machines
00:28:08 6 See also
00:30:03 7 Notes
00:30:44 8 References
00:31:22 9 External links
00:32:18 Recognizing partial solutions
00:33:44 Oracle machines
00:34:07 See also



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SUMMARY
=======
In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running (i.e., halt) or continue to run forever.
Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist. A key part of the proof was a mathematical definition of a computer and program, which became known as a Turing machine; the halting problem is undecidable over Turing machines. It is one of the first examples of a decision problem.
Informally, for any program f that might determine if programs halt, a "pathological" program g called with an input can pass its own source and its input to f and then specifically do the opposite of what f predicts g will do.  No f can exist that handles this case.
Jack Copeland (2004) attributes the term halting problem to Martin Davis.