Universal computation is the set of all computable functions that can compute the set of all computable functions.
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Replying to @Plinz
Does the function that can compute all the functions that cannot compute themselves belong to this set ?
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Replying to @vakibs
No, it really just a friendly set of computable functions, like the Turing Machine or the Python interpreter or the Game of Life.
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Replying to @Plinz
Computable functions in a finite amount of time? Or just computable functions without worrying whether the machine will halt or not ?
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Replying to @vakibs
A function that cannot be computed in a finite amount of time is not computable.
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Replying to @Plinz
What about a function which computes in a finite amount of time on a Turing machine for some inputs and which does not halt for some other inputs? There are uncountably many functions like that..
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Yes, a computation that does not halt does not compute a computable function. Note that only the transition function of your computer is actually implemented, everything else exists only as the observer's interpretation. We can often not decide if an interpretation applies.
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