$[10$ marks total$]$

a$)$ Construct a CFG where $L(G_1)=0$@$1^{2n}{0}^n,n0.(2$ marks$)$

b$)$ Prove that $L(G_1)$ is not regular. $(4$ marks$)$

c$)$ Design a PDA $P_1$ such that $L(P_1)=L(G_1).(4$ marks$)$