With Σ = {a,b}, give a dfa for L= w1aw2 : |w1 |≥ 3, |w2 |≤ 5}


I racked my brain,I saw other people’s solutions and it don’t make sense. I think my biggest problem is I don’t know when one string ends,like for example w1 is >=3 and it can have how many ever b’s or a’s as long as it’s 3 and above,so when do we get to have the First a that’s after the W1?how do I make sure it’s not a part of the W1? that’s whats so confusing the W1 string can have as many a’s as it likes which means it should have an a loop,but you can’t have an a loop cause YOU NEED 1 A EXACTLY after the W1 string. this is a catch 22,damned if you don’t damned if you do..help please I spent an hour on this to no avail. I tried every possible thing and saw people’s solutions and I feel like when they solved it they are either dismissing what I mentioned above,or something is going COMPLETELY over my head.