Greeting, I have problems understanding the assignment in the field of automata theory and formal languages.
The task says:
Construct a minimal DFA that accepts the following languages:
It is necessary to implement an automaton for the language $L_3$. My solution is shown above.
What interests me here is whether the automaton should accept a word such as $babababbabbb$.
To satisfy $L1$ a word must start and end with the same letter to be accepted. To satisfy $L2$ the word $w$ must not contain the substring $bbb$ to be accepted.
Now I'm interested in whether the word $babababbabbb$ will be accepted? This word starts and ends with the same letter, and if we look at the word between the first and last $b$, we have that word does not contain the substring $bbb$, but if we look at the whole word, it contains the substring $bbb$, so that confuses me.
Thanks in advance!