# How to find out the complement of a language of turing machines?

With only using our thinking. What do I have to think about when finding a complement of a Turing machine for example.

L={M∣M is a TM that halts on empty tape after even transition steps} What's the complement of L would it be:

1. L={M∣M is a TM that does not halt on empty tape after even transition steps}
2. L={M∣M is a TM that halts on empty tape after odd transition steps}

Please give me your train of thought when coming up with a complement for an automaton.

• You're not being asked to find the complement of a Turing machine. You're being asked to find the complement of a language. – Tom van der Zanden Oct 3 '19 at 12:22
• @TomvanderZanden Oh okay, I see where I made a mistake. – alexW Oct 3 '19 at 23:38

You cant find the complement of a $$TM$$ for undecidable languages. A decidable language is such that a $$TM$$ which recognizes language membership, always halts with a yes. In this case finding the complement of the machine is simple, just reverse the yes with the no, obtaining the complement of the original decision problem. I leave to you the task of determining whether the language of your example is decidable or not.
HINT: you can compare it with the Halting problem or $$ATM$$