Given the context free grammar $G=(\{S,A\}.\{0,1\},S,P),$ where $P$ is given by:

$S$AOA

A$->$ AA $|$ OA$1|1$AO $|0|||$

$($i$)$ Give the description of an equivalent pushdown acceptor as a $7-$tuple.

$($ii$)$ Give the transition diagram with all the possible transitions.

$($iii$)$ Give the leftmost derivation on a string $10100$

$($iv$)$ Show the equivalent moves on the pushdown acceptor as a series of configuration moves leading to acceptance.