$3.(5$ points$)$

Given the following final$-$state DPDA,

and the following strings

which of these strings are accepted by the given final$-$state DPDA? Put your answer in the following blank.

$(1\mathrm{.}5$ points$)$

If the given final$-$state DPDA is considered as an empty$-$stack NPDA $($state $0$ is no longer a final state$),$ then which of the given strings are accepted by the empty$-$stack DPDA? Put your answer in the following blank. $(1\mathrm{.}5$ points$)$

Now, consider the following two general questions. First, what is the language $\backslash ($ L$\_\{1\}\backslash )$ accepted by the given final$-$state DPDA? Put your answer in the following blank.

$\backslash [$

L$\_\{1\}=$

$\backslash ]$

Second, what is the language $\backslash ($ L$\_\{2\}\backslash )$ accepted by this DPDA when viewed as an empty$-$stack DPDA? Put your answer in the following blank.

$\backslash [$

L$\_\{2\}=$

$\backslash ]$

$\backslash ($ L$\_\{1\}\backslash )$ obviously is bigger than $\backslash ($ L$\_\{2\}\backslash ).$