How to design a DFA of all strings over (0,1) such that every block of 5 consecutive symbols contains at least 2 0's?
The question asks HOW TO DESIGN, you don't have to write the whole DFA, but you can if you want to. Just describe how you would design.
There are 32 strings of length 5. Some of them do not contain at least two 0s, some do. Those that do not contain at least two 0s should lead to the DEAD state (from which there is no return). But those that do have at least two 0s should lead to a state that checks another block of 5 symbols.
Try to draw a binary tree of depth 5, with 0 as the left child and 1 as the right child for each node. Does it help design the DFA? For simplicity first try to design for blocks of 3 symbols not 5.