$zax|bY||$

Convert the following CFG into CNF$.(10$ points$)$

$S$axxbY

$x$abx$|a||$

$YbbY|b||$

Part III: $(30$ points$)$

Convert the following FA into a PDA. $(10$ points$)$

Build the PDA accepting the same language as this CFG $(10$ points$)$

$s$xaxb

$xax|bx{|}^{{?}^{?}}$

Draw the trace of PDA $($State$,$ Stack and input Tape$)$ in a table format when the following PDA processes the following input string aabcbaa. Note that the input alphabet is $\{a,b,c\}.(10$ points$)$