TOC TM Decidiblity

Question

Is it decidable whether a given Turing machine accepts a recursive set?​​ explain with an example .

Comments

please explain what is decidablity ?

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Decidability is like saying yes/no to such a question. Whether we can sort a finite size array, whether there exists a shortest path in a graph etc are decision problems. If we can always say either yes or no to such a problem, it is decidable. Even for one instance of the problem, if we cannot decide between yes and no, that problem is not decidable.

Answer 1

"whether a given Turing machine accepts a recursive set"

It is a monotonic property. So, if all superset of recursive set is recursive ? No, it could be recursive enumerable.

it will be satisfying non monotonic property of Rice theorem, it is undecidable and non recursive enumerable

Comments

then what if question asks "whether a given Turing machine accepts a regular set" ??

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See what I think superset of regular set ∑* , we cannot get any string more than this . So, superset of regular set is regular . I think so.@vijay. What do u think?

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I am confused ... as u mentioned above super set of recursive is r.e. so i thought why not super set of regular is r.e. so it should also be undecidable for TM. ??