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Taxtro
Computerphile
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Comments by "Taxtro" (@MrCmon113) on "Turing Machines Explained - Computerphile" video.
That is a description of a Turing machine. It's just unnecessarily complicated. The employees are the states and the split in the stack marks the position of the read-write head.
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Correct, quantum computers are exactly as powerful as turing machines or lambda calculus.
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True. Other automata like pushdown automata are more relevant to actual applications. Turing machines are just a very simple way of describing something very powerful, but the way one would work on a specific task is unnecessarily complicated. There is no reason to mimic Turing machines in technology.
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Exactly. The configuration of the automaton is different from it's state. At any moment the automaton has a configuration, and that consists of it's state and the position of the read/write head on the tape.
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The transition functions are not read; the Turing machine knows them from the start and all of the time. Nor is it important that the alphabet is 1s and 0s. You can expand the alphabet as you wish without the machine becoming any more powerful.
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I don't know what you mean with simulating memory. The Turing machine is essentially a function. You give it an input string and it may give you an output.
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A Turing machine is a kind of automaton.
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As far as I know Quantum computers are still theoretical, but it was proven that they are just as powerful as Turing machines. Also you should know that there is nothing special about that model in particular. GOTO (if statements), WHILE programms, lambda calculus and many other things are just as powerful as Turing machines and quantum computers as well. As for automata, which are less powerful than Turing machines, those are finite automata or pushdown automata for example.
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Yeah it has been proven that quantum computers are no more powerful than Turing machines; either the guy in the video didn't know about it or he left it out for some reason.
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I think the video was somewhat misleading. Turing machines aren't really relevant to technology, but rather to theoretical considerations. A Turing machine is a very simple way to describe a very powerful system, but there are much better ways to implement most (interesting) functionalities in practise.
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Those programs are translated into assembler code, which is itself Turing complete. I think it is closely related to GOTO statements, which are also just as powerful as Turing machines.
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