Let $=\{0,1\}$ and L $=\{$w $|$w in $,|$w$|1|$w$|0+1\}.$ As usual, here and elsewhere, $|$s$|$x denotes the number of times the symbol x appears in the string s$.$

$*$Keep in mind that this language can allow strings with any number $0\text{'}$s as long as there is a greater number of $1\text{'}$s $($e$.$g$.$ s $=0001111,1111000,000111011).$

$1\mathrm{.}1$ Construct a CFG that generates L$.$

$1\mathrm{.}2$ Construct a PDA that accepts by empty stack the language L and show its transition diagram.

$1\mathrm{.}3$ Using IDs, show that the input sequence $110101$ is accepted by your PDA.