show all steps dont give just answer. for rmd$,$lmd show the steps $.$ give hand written answera$)$ The language generated by the grammar $($list all strings of length $5)$:

$SA$

$A$aAa

$AB$

$BbBb$

$Bc$

b$)$ For the following grammars and string s$,$ give

$($i$)$ a parse tree

$($ii$).$ a left$-$most derivation, and

$($iii$)$ a right$-$most derivation.

$SAB$

$AaA$

$Ac$

$BBb$

$Bd$

String $s=$ aacdb

a$)$ Write down Chomsky Normal Form$($CNF$)$ for the following context free grammar.

$Sax|Yb$

$AS|$

$Yb|b$

d$)$ Convert the given CFG to GNF$.$

$SMN$

$M$aMb$$

$N$aNb$|$

$($Answer any two questions$)$

Prove that the language w $B$ is a string of $0$ and $|s$ is context$-$free by designing a PDA

that accepts it$.$

b$.$ Discuss the relationship between the non$-$terminals, terminals, and stack symbols in a PDA that

accepts a CFG$.$

c$)$ Show how to convert the $CFG$:$S$ aSb $|SS|$ into an equivalent PDA.