$($VII$)$ Create a PDA that recognizes the following context free languages with terminals $\{a,b,c\}$

$L_1=\{c^{k}w|win\{a,(b){\}}^{**}$ and $k=|w|\}$

$L_2=\{a^{n}b{c}^{2n}|n>0\}$

$($i$)$ Describe your algorithm

$($ii$)$ Give the description as a complete $7-$tuple with a transition diagram

$($iii$)$ Show configuration sequences on a string of length$>2$ leading to acceptance.