Here i have considered 3states to be A,B and C. As they have asked for #dfas that generate empty languages. (A is always initial state)
we will have 3 cases :
1)no final state that yields 729 DFA.
2)two final states that gives 81 DFA.
3)one final state and we will have four cases(here) = 2 * 144+2*4=296 DFAwe will have two more case of case 3. means 3.3 and 3.4.
when state A is isolated and there is transition from state C to state B.(because for 3.1 we have not considered transition to state B from C).
so we will have two cases for final state where it either has transition to itself or state C but not to state A as it will not satisfy empty strings relation than.
|
a |
b |
A |
1 |
1 |
B (final state) |
2 |
2 |
C |
1 |
1 |
so here will have 4cases .
similarly for C (final state )we will have 4state.. )
so total #DFA= 729+81+296 = 1106 DFA.