Easy Warm$-$up #$1$: Prove the following: A language $x$ is the language of an alternating TM with $O(logn)$ space and $O(1)$ alternations if and only if $x$ is in NL$.$

Easy Warm$-$up #$2$: A boolean circuit is called a formula if its directed graph is a tree. In Lecture $13\mathrm{.}4$ we proved that any polynomial$-$size formula is equivalent to some $N{C}^1$ circuit. Here we ask you to prove that any $N{C}^1$ circuit is equivalent to a polvnomial$-$size formula, which also has $O(logn)$ depth.