Turing's halting theorem | Wikipedia audio article

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 Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago. Learning by listening is a great way to: - increases imagination and understanding - improves your listening skills - improves your own spoken accent - learn while on the move - reduce eye strain Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone. Listen on Google Assistant through Extra Audio: https://assistant.google.com/services/invoke/uid/0000001a130b3f91 Other Wikipedia audio articles at: https://www.youtube.com/results?search_query=wikipedia+tts Upload your own Wikipedia articles through: https://github.com/nodef/wikipedia-tts Speaking Rate: 0.9360051123447805 Voice name: en-US-Wavenet-C "I cannot teach anybody anything, I can only make them think." - Socrates 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.