Language accepted by DFA

Question

Comments

Every string Ending with bba = bbaa is not accepted

Every b follows atleast 2a's = baaa is not accepted

Every b follows exactly 2a's = answer

Every string has the substring baa =baaaa is not accepted

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If there is no b at all that string also be accepted. . But here string 'a' is not accepted . . Why so??

Answer 1

I have given a number to each of these stages for convenience, Now let's look at each state one by one

1.) (ON a) Goes to 1 only and (ON b) goes to state 2 (So, b shall always be accepted first every time we iterate through this DFA)

2.) , 3.) , 4.) (THEY WILL NEVER ACCEPT "b" "b" "a" respectively this will always end up in the Dead State 5.)

Therefore, 2.) & 3.) will always accept ONLY "a's" in the substring.. and 4.) will return a "b" every time to state 2.) and Cycle goes on and on..

Now look everytime I used the words "Always accepted" in my answers, and you will figure out the right choice

So, Every b follows Exactly 2 "a".  .. (C)

 

Comments

Acceptance of a string means to accept the strings in the language and to reject the strings it's language doesn't have.  

Here 'evry b follows exactly 2a's ' but if b itself is not in the string then there is no restriction. Thus the language becomes all a's AND (as u say) b's follows exactly 2 A's but this is not accepted by the automata. . The initial state must be one of the final states. . To include all A's alone

Am I right or not?

@Namit Dhupar

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Until and unless you do not reach the final state (4) You cannot say it's accepted or rejected!
and ofcourse "b" is in the string!
1-----^b----> 2    
There is no other way State 1 can reach state 2 if you don't give "b" as input!!!