$3.(15$ points$)$ Given the following grammar with production rules numbered from $1$ to $8,1.S0A,$

$2.$S $1A,$

$3.SA0,$

$4.SAB,$

$5.$S $0,$

$6.$S $0$A$1,$

$7.$ A $1,$

$8.S$

$($i$)$ Indicate which of the rules satisfy the conditions for a context$-$free grammar $($Sample answer: Production rules $1,5,8)$;

$($ii$)$ Indicate which of the rules satisfy the conditions for a left linear grammar;

$($iii$)$ Indicate which of the rules satisfy the conditions for a right linear regular grammar;

$($iv$)$ Indicate which of the rules satisfy the conditions for a linear grammar.