Give DFA's accepting the following languages over the alphabet$\{0,1\}$,The set of all strings such that each block of five consecutive symbols contains at least two 00s. This question is from Automata Theory,Languages, and Computation.
I have tried to use 11 states but it's wrong obviously. And I'm not sure about whether it's right to accept the strings that contain less than five symbols.
Hint. It is easier to first compute a DFA for the complement of your language, which is the set of all words containing a block of five consecutive letters containing at most one $0$, that is, containing one of the following blocks: $11111, 01111, 10111, 11011, 11101, 11110$. That is, the complement of your language is $$ \{0,1\}^*(11111 \cup 01111 \cup 10111 \cup 11011 \cup 11101 \cup 11110)\{0,1\}^* $$ Good luck to find the DFA, which has, if I am not wrong, 16 states.
P.S. To answer your last question, yes, words of length $< 5$ are in your language since they do not contain any block of length $5$.
