turing computable function

Question

Here are few True False questions: Somebody please answer these:

Let F(0) = 1, and let F(n) = 2^F(n-1) for n>0. Then Is F Turing-Computable?
No language which has an ambiguous context-free grammar can be accepted by a DPDA. Is this true ? If not which grammar is that.

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is this a Physics question ? – Raptor Dec 07 '12 at 02:31

score 0 · Answer 1 · answered Dec 07 '12 at 02:36

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I guess the first one is true.

According to the Church–Turing thesis, computable functions are exactly the functions that can be calculated using a mechanical calculation device given unlimited amounts of time and storage space. Equivalently, this thesis states that any function which has an algorithm is computable.

answered Dec 07 '12 at 02:36

redswallow

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Thank you for the answers. However If that is the case, Every function that can be mathematically defined is Turing computable? – Niraj Rana Dec 07 '12 at 04:29
Apparently according to numerous reviewers unless a computation is [Pure function](https://en.wikipedia.org/wiki/Pure_function) it may not be a computable function. – polcott Jul 17 '22 at 01:57

score 0 · Accepted Answer · answered Dec 07 '12 at 02:55

For (1), ask yourself this question: could you write a computer program that could compute this function? If so, then by the Church-Turing thesis, then you know that there must be a TM that could do the same computation, so the function is computable. If not, then you know that no TM could evaluate the function either.

For (2), remember that ambiguity is a property of grammars. There can be multiple grammars for the same language.

Hope this helps!

turing computable function

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