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Jan 2, 2017 at 8:15 comment added Will Sawin No, this doesn't work, for exactly the reason you state. It's not possible to enumerate polynomial-time Turing machines in the way you are suggesting - telling if a fixed Turing machine halts in polynomial time - as this would enable you to solve the halting problem by considering Turing machines that ignore their input and hence either halt in constant time or run forever.
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Dec 3, 2016 at 2:20 history answered none CC BY-SA 3.0