Is there a slowest growing uncomputable function?

Asked Jul 12 '22 at 23:10

Active Jul 13 '22 at 00:06

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The question Is busy beaver the fastest growing function known to man? is answered negatively, pointing out that arbitrarily fast growing functions can be constructed.

But is there a "reachable" lower bound for uncomputable functions, or can the growth rate be just e.g. endlessly halved while still remaining uncomputable?

edited Jul 13 '22 at 00:06

asked Jul 12 '22 at 23:10

2080

Undecidable decision problems (e.g. the halting problem) can be represented as functions that return a single bit. That's $O(1)$, which is quite slow-growing. – Pseudonym Jul 13 '22 at 00:58
Are you two taking the same class, by any chance? – Yuval Filmus Jul 13 '22 at 10:54
Nope, I just came across the busy beaver question and wondered – 2080 Jul 13 '22 at 13:22

Is there a slowest growing uncomputable function?

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