Consider the regular grammar G$($Z$)$ given by the following rules:

Z:$=$ U$1/$Vo$/$Zo $/$Z$1$

U:$=$ Q$1/1$

V:$=$ Q$0/0$

Q:$=$ Q$0/$Q$1/0/1$

Note: Alternate $1$ and $0$ for a and b respectively as subscripts in the regular grammar G $($Z$)$ defined in c above.

i$.$ Draw the state diagram with appropriate FA commands for G $($Z$)$

ii$.$ Inductively present the algorithm for the DA minimisation

iii. Parse the following strings to determine if they are valid for G$($Z$)$

$0101$

$01001$

iv$.$ Make distinctive comments $/$ remarks on $($ i and iii$)$ above