Push Down Automata that recognizes language

Question

I'm struggling on how to use the stack for this push down automata problem. The problem is to design a PDA that recognizes the language: $$A = \{a^ib^{2i}|\,i>0\}$$

So, we will be pushing a's onto the stack until b arrives, then how do you determine double the amount of b's for each a?

Answer 1

have a stack that recognizes 2 symbols for 'a', first beginning from the left reading all the a's and pushing 1 a onto the stack for each a then once you reach the first b, if there is a 'a' on the stack then change it to say a 'ha' <- for half a, then move right, if there is another b we can now pop the 'ha' off the stack and continue, if there is a 'a' we go to a rejection state/a loop of some form, if we reach the start symbol we have passed the test!