ACE ACADEMY: TOC

Question

How many 2 state DFA’s with designated initial state can be constructed over the alphabet Σ = {a, b} that accept empty language ϕ ?
(a) 4       (b) 16     (c) 20       (d) 24

Comments

is it 16?

---

what does designated initial state means ?

---

intial state can be chosen in only one way.

---

means if we select A as initial state in DFA1 then in DFA 2 also A will be the initial state ?

---

https://gateoverflow.in/16808/many-state-drawn-over-alphabet-which-accepts-empty-language

---

Initial state has been already defined and that initial state can accept the empty language

Answer 1

We should deal this type of questions using State transistion table

Answer 2

case1:when no final state to be chosen.

    then dfa possible=2^4=16.

case2:when X is initial state and Y is final state but unreachable from X

  then dfa possible =2^2=4

therefore in total dfa possible is =16+4=20.Ans

Comments

But initial state can accept the empty language means initial state is also a final state right ??

---

@Srken In Empty language there are no strings present right 

you are confusing between Empty language and Empty string

Dfa has initial state as final state if it accepts Empty string ϵ and not Empty Language