push and pop operation in PDA

reference : https://www.youtube.com/watch?v=m8a3l5t8ok8#t=3.387

if we take the string aabbaa , for the first a PDA pushed the a & it remains at state Qs, but for second PDA changed its state from Qs to Q1. So how the reaming string is pushed and poped in the stack????

Sougatamoy Biswas @sougatamoy
28 Jan 2016 12:27 pm

This is NPDA. There is two options for 2nd 'a'  (a,a/ε) or (a,a/aa) . It may go to the next state or it may push 2nd a also remaining the same state.