Problem 1 In this question the alphabet is fixed as {a,b}. Write a regular expression for the language of strings containing a's only when they occur as part of a block of consecutive a's of even length. Thus the legal strings cannot contain an a by itself or a sub- string of 3 or 5 or 7... consecutive a's. Thus baabbb is accepted, so is aabaabaaaabbaabbaa and so is bbbbbbb which has no consecutive pair of a's. However baaab is not allowed as this has three consecutive a's nor is bababaab or baaaaab. Design a DFA (not an NFA) for this language. A picture is preferred. You must show the dead state if there is one. For full credit your machine must have no more than 3 states including the dead state (if there is one)