# turing machines – Complexity of the language that enters an infinite loop

A few days ago I had a test that I failed to pass, and it had a question that I failed to do.

This is the question

Let’s look at the language $$L_loop =$${
$$left langle M,w right rangle$$ | When M is activated on the input w, the machine M enters an infinite loop }

We will mark our input length: $$|left langle M,w right rangle| = n$$. Determine which of the claims is correct:

1. The language is in $$P$$
2. The language is not in $$NP$$ or $$CoNP$$.
3. The language is in $$NP$$ but not in $$NPC$$.
4. The language belongs to $$CoNP$$.
5. None of the above claims are true.

From what I understand in the question, there is a language that accepts Turing machines that go into an endless loop.

1. It cannot be, if the machine works infinitely, it is impossible to know in polynomial time when we will get yes and when we will get no. It has no algorithm.
2. Probably can not either. A problem will be in NP if it has a non-deterministic guessing algorithm. If a witness gives input, it is not possible to say yes to the answer, because it is infinite.
3. Do not know about it, maybe he is right
4. Language should belong to Conp only when a guessing algorithm should say no. And I do not know if here should be said no and then it’s CoNP or say yes and then it’s NP.

I tried to figure out what the answer might be, but I could not figure out the answers to the question.

Maybe 5 is right, because I could not tell everyone else that they were right