I need to construct a deterministic finite automata, DFA M, such that language of M, L(M), is the set of all strings over the alphabet {a,b} in which every substring of length four has at least one b.

Note: every substring with length less than four is in this language.

For example,

aba is in L(M) because there are no substrings of at least 4 so every substring of at least 4 contains at least one b.

abaaab is in L(M) because abaa, baaa, aaab all contain at least one b

abaaaa is not in L(M) because aaaa does not contain at least one b

Hint: Use the complement