$2.(4$ points$)$

The language accepted by the final$-$state PDA shown in Fig. $1$ below is:

$(1$point$)$

The language accepted by the final$-$state PDA shown in Fig. $2$ is:

$(1$ point$)$

The language accepted by the following final$-$state PDA is:

$(2$ points$)$

To convert a final$-$state PDA to an empty$-$stack PDA, we put it between a new start state $\backslash ($ S $\backslash )$ and a new state $\backslash ($ E $\backslash )$ and define some new edges and new transition instructions for those new edges. For instance, for the final$-$state PDA shown in Fig. $1,$ we would get the following empty$-$stack PDA.