# Check if $L = \{ <M>$ : $M$ simulated on $<M>$ halts after max. $32$ steps $\}$ is decidable

The confusing part is, that $$M$$ basically is simulated on its own encoding $$\langle M\rangle$$. Nevertheless, I would claim its decidable by simply creating the following $$TM$$ $$T$$:

check if $$\langle M\rangle$$ is correctly encoded
Build a $$TM$$ $$M$$ with input $$\langle M\rangle$$
Simulate $$M$$ on $$\langle M\rangle$$ for $$32$$ steps
if $$M$$ halts, $$T$$ accepts, otherwise $$T$$ rejects.

This is totally straightforward, thus I am quite unsure. Any hint is highly appreciated!

• this looks correct Jun 28 at 13:07