# Create a transition system where every sequence has at least twice as many $a$'s than $b$'s

Create a transition system with edges $a$ and $b$ and an initial state, such that for all possible sequences, you have that: The amount of $a$'s in the sequence is at least twice as much as the amount of $b$'s in the sequence.

I'm really not sure if I did it correctly because I just had DFA and NFA and other kind of automata last semester and they still confuse me for this. My problem is, do I have to make sure that in this task that my transition system needs to create every possible sequence where we have at least twice as many $a$'s than $b$'s? Or as the task says, all I need to make sure is that for every sequence, we have that there are twice as many $a$'s than $b$'s? I think this is it and that's why I created this transition system:

Did I understand it correctly and is my transition system correct? Or do I really need to create a transition system which generates every possible combination of $a$'s and $b$'s satisfying the condition mentioned in the task? :S

• What you have satisfies the question. It's actually a bit more than you need, with the three edges that go in a tight loop to the node that they started from. – Daniel Martin May 25 '18 at 17:03