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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
in Theory of Computation by Active (3.5k points)
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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 ?

1 Answer

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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

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