Empty language = { } or $\phi$
condition : 1 No final States
|
p |
q |
q |
a0(Initial state) |
a0/a1 |
a0/a1 |
a0/a1 |
a1 |
a0/a1 |
a0/a1 |
a0/a1 |
In that case , we doesn't have any final state...so every input we have 2 choices either we go to state a0 or a1
therefore , 2 x 2 x 2 x 2 x 2 x 2 = 26 ways
since no final states therefore it accepting the empty language
Condition : 2 a1 is a final state
|
p |
q |
q |
a0(Initial state) |
a0 |
a0 |
a0 |
a1 (final state) |
a0/a1 |
a0/a1 |
a0/a1 |
here , if a1 is final state then if we are in state a0 ...and In any input we doesn't change our state from a0 to a1 ..cuz a1 is final state , therefore it's accept the string but here we only accept the empty language right ??
therefore , when we are in a0 state we have only 1 choice .. in any input p , q ,r we stay in the same state which is a0
but when we are at state a1 state we have 2 choices either we stay in a1 or go to a0 state
therefore , 2 x 2 x 2 = 23 ways
Total number of ways = 26 + 23 = 72 ways