Question: Find a finite automaton that accepts bit strings such that every sequence of four consecutive characters contains a 1.
Answer: This is the set of all bit strings that do not include 0000 as a substring. The following accepts all strings including 0000 as a substring, if the start state is a and e is the accepting state.
____
0 0 0 0 L 0,1\
a ----> b ----> c ----> d ----> e ----/
^ / / /
|<----/1 /1 /1
|<------------ /
\___________________/
To convert it into an automaton rejecting all strings including 0000,
we make the accepting states be a, b, c, and d.