# Is this set computable?

Let be $$B$$ a Busy Beaver function and set $$W=\{\langle M \rangle :\text{M stops in less than B(10^{1000}) steps on an empty tape}\}$$. Is this set computable?

I'm not sure how to approach this question. I suspect that this set is computable and have tried to see if it is finite, but haven't reached anything.

• I don't understand the definition of $W$. What is $M$? – Yuval Filmus Aug 21 '19 at 21:01
• Hi @YuvalFilmus is a turing machine, thanks! – PCG Aug 21 '19 at 21:10
• Let me phrase this differently. When does an integer $n$ belong to the set $W$? – Yuval Filmus Aug 21 '19 at 21:12
• @YuvalFilmus when $n$ is a number of a turing machine (is a similar numeration of a Gödel numeration) and tha Turing machine with number $n$ stop with input the empty tape and stop in less $B(10^{1000})$ steps. – PCG Aug 21 '19 at 21:16

Your function is computable. Just run the input machine on the empty input for $$B(10^{1000})$$ steps. Note that $$B(10^{1000})$$ is just a constant which can be hardcoded into your code.