decidability

Question

L1={<x>| x is accepted by the given turing machine M}
is L1 decidable?
plz explain your approach

Answer 1

It is not necessarily decidable since Turing acceptable languages are also known as recursively enumerable languages.And there are languages which are recrsively enumerable but not recursive.Also we know that recursive languages are decidable(also known as Turing decidable).

Based on the above mentioned reasons , we can hence conclude that L1 is not decidable since all recursively enumerable languages are not recursive and hence not decidable.

Comments

yes i thought the same thank you :)
actually this is linked to another question
L1={ <M>|M is a turing machine such that L(M) is equal to L2}
L2 is some other given language.
what do you think regarding this

Answer 2

No L1 is not decidable

L1 is said to be decidable if it is accepted by Halting Turing Machine

Any Language is said to be decidable if there exist HAlting Turing M/c means on Yes it Say Yes on No it says No

But if a language is accepted by Turing Machine

That means it is Recursively Enumerable

on string acceptance M/C will say Yes

but on Streing Rejection it May say no or it can Fall in infinte Loop

Comments

yes i thought the same thank you :)
actually this is linked to another question
L1={ <M>|M is a turing machine such that L(M) is equal to L2}
L2 is some other given language.
what do you think regarding this

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L1 is undecidable

it is Halting problem