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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If we want to exclude such functions (or restrict their domains), we have to proceed in a comstructive manner by defining valid input zones, marking the territory of natural numbers of acceptable areas. Is there a proof that different constructive processes yield the same zones?
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I am wondering if that the "computability" framework will run into similar paradoxes as the previous frameworks based on mathematical specification.
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I think automata theory is pretty solid :)
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