Test by Bikram | Theory of Computation | Test 2 | Question: 29

Question

The number of possible finite automata with two states $a0$ and $a1$ (where $a0$ is always the initial state over the alphabet $\{p, q\}$) which accepts empty language is _______ .

Comments

This will help you

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Those who are wondering about this pic and scratching head how 20?

First of all, there is a0 where 2 combination possible either p loops on a0 or goto a1, similarly we have choices of q on a0 either to loop or goto a1 and forwarding that logic to a1 also we in total (2*2*2*2) 16 such combinations.
**take your time to get these lines first, try to draw 1 or 2 combinations, you'll get them."

Now, we got to choose the final and non-final state and final state, which gives us 4 combinations, now read the question the last line "accepts empty language", 3rd and 4th Combinations is accepting more than "empty means nothing"i.e at least they are accepting $\lambda$ so, they are out.

No, combination-1 is clearly an empty language accepting FA as there is no accepting state so, 16 are these combinations. Going towards combination-2, which is further explored below, out of 16 only 4 are shown which are favorable to accept "empty language" (4 comes from here).

So total 16+4=20

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@Arjun sir

please give proper solution