$3$C$)$ Show that language $L=\{a^n{b}^n{c}^n|n1\}$ is not CFG using pumping lemma.

$4$A$)$ Construct a PDA for the $CFGG=(\{S,A,B\},\{0,1\},S,\{S0A,A0AB|1,B1\})$ and show the sequence of moves for the string $"000111".$

$4$B$)$ Construct NPDA for the language $L=\{win\{a,b{\}}^{**}$:$n_a(w)=n_b(w)\}.$

$4$C$),$ Construct DPDA for the language $L=\{a^n{b}^{2n}{c}^n{d}^{2n}|n1\}.$

$5$A$)$ Design a Turing Machine using the state transition diagram to reverse a given sring $w\{0,1\}+$ such that the input tape will contains final state followed by reversed string.

$5$B$)$ Design a Transducer using state transition diagram to compute the sum or differenc of two positive integers, $x$ and $Y.$ The integers are represented in the Turing machine with equal number of $1\text{'}$s separated by $0.$

$5$C$)$ Construct a Grammar to generate a language $L=\{a^{nbn}{?}^{n}m|n,m1\}.$