$($A$)$ Using the method shown in the proot of Theorem $2,$ construct a regular grammar that generates the language accepted by this finite$-$state automnton $($machine$).$

$($B$)$ Uoing the method shown in the propt of Theorem $2,$ construct a $($nondeternainistic$)$ finite$-$state autom ation $($machine$)$ that accepts precicly the language generated by the regular grammar shoux

$S0$

$SiB$

$S0A$

$A1A$

$AOB$

$A1$

$A0$

$B1$