a$.=1=c$

$y-4$

$*)d=i$ M a Eer $4=.$

$y$ cescis

$9x+x=1=1$MODULE $4$

Construct the CFG for the given language. Illustrate the parse tree, Leftmost

derivation and right most derivation for the given string.

a$)L=\{\begin{array}{c}{a}^{\text{'}}b{c}^k|ji+k\end{array}$ and $\{$:$i,j,k0\}$

b$)$ R$.$E $=00{11}^{\text{'}}$

Construct the CFG for the given language. Illustrate the parse tree, Leftmost

derivation and right most derivation for the given string.

a$)L=\{a^n{b}^{2n}|n>0\}$

b$)L=\{\begin{array}{c}{0}^{a}10^c|a+c=b\end{array}$ and $\{$:$a,b,c0\}$

c$)L=\{a^n{b}^m{c}^n|n,m>0\}$

Find the CNF for the given CFG$.$

$S$ ASB $|$

$A$aAS$|a$

$BSBS|A|bb$

Find the CNF for the given CFG$.$

$SAB|AC$

$A$Bab$|$

$B$BAa$|$

Construct a grammar in Chomsky Normal Form for the following CFG G $,$

$C.$ Show the intermediate steps in construction.

$S$ABC

$ABC|a$

$B$bAC$|$

$C$CAB$|$

Convert to Greibach Normal Form for the given grammar $G=\{\begin{array}{cc}{A}_1,& A_2\\ 0,& 1\\ P\end{array}.$

A$1).$ where the $P$ consists of the following.

$A_1{A}_2{A}_2|0$

$A_2{A}_1{A}_1|1$

Convert to Greibach Normal Form for the given grammar $G=\{\begin{array}{ccc}{A}_1,& A_2,& A_3\\ 0,& 1\end{array},$

$\{$:$P,A_1\},$ where the $P$ consists of the following.

$A_1{A}_2{A}_3$

$A_2{A}_3{A}_1|b$

$A_3{A}_1{A}_2|a$

Convert the grammar $SAB,ABSB,ABB,B$aAb,$Ba,Ab$

into Greibach Normal Form.MODULE $3$

Find the Regular Expression corresponding to the given automata.

Let $r1,r2$ be regular expression. Prove that there exists a $-$NFA for the following

cases and explain the construction procedure.

a$.r1+r2$

b$.$ r$1.$r$2$

c$.r1\{N\}\{$ Hint: $\{N\}$ indicates that $r1$ is matched exactly $N$ times $\}$

d$.r1?\{$ Hint: $r1$ is matched at most once $\}$

Show that the language is not a regular. Justify.

a$)L=\{\begin{array}{c}{0}^n|n\end{array}$ is a perfect square