Question $2$

Let $L=\{\begin{array}{ccc}(\text{:}{A}_1,& \text{d}\text{o}\text{t}\text{s}\text{,}& A_k\text{:})\text{:}{A}_1\\ \text{d}\text{o}\text{t}\text{s}\\ A_k\end{array}$ be DFAs over the same alphabet $$ and $.$

Prove that Lin PSPACE. You can use the fact that PSPACE $=$ NPSPACE that will be proved next

lecture.$($Actually$,L$ is PSPACE$-$Complete, but that is beyond the scope of an exercise$).$