Self_doubt

Question

C1: For DFA (ϕ, Ʃ, δ, qo, F),
         if F = ϕ, then L = Ʃ*
C2: For NFA (ϕ, Ʃ, δ, qo, F),
         if F = ϕ, then L = Ʃ*
Where F = Final states set
ϕ = Total states set

Choose the correct option ?

• A. Both are true
• B. Both are False
• C. $C1$ is true, $C2$ is false
• D. $C1$ is false, $C2$ is true

What is the answer and also explain that?

Answer 1

Option c 

In case of dfa if all states are final states then it accept set of all string  (E) ^* .

In case of nfa it becomes false 

Answer 2

C1: For DFA, if all the states are final states, that would mean it accepts $\sum ^*$ as in case of DFA, transitions are defined for each and every alphabet and for each and every set.

C2: But in case of NFA, transitions are not defined for all the states and only the meaning of the language can be conveyed. So, if all its states are final states then we can't say it accepts $\sum ^*$ as we don't know about other states.

Hence,(c) C1 is true and  C2 is false is correct.