For the following language, prove, without using Rice's Theorem, whether it is in D, SD but not D, or not in SD.

Question

The following language is: $L = \{<M>|¬L(M)∈D \}$

Let's say there is a TM called regTM.

regTM = $\{<M>|L(M) $ is regular$ \}$

I know that regTM is undecidable, therefore I am led to believe any TM for L would also be undecidable.

How would I prove this, without using Rice's Theorem?

Answer 1

Um why think about regular languages?

Hint

Can $L$ be enumerated? If it can, can you construct a TM that decides whether a program $P$ halts on an input $X$ or not? You can easily simulate $P$ on $X$ and if it halts you would observe it, so can you given $P$ and $X$ computably construct a program $Q$ that accepts an undecidable language iff $P$ does not halt on $X$?