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hello everyone in this lecture we are going to discuss about an example for pda so we have to construct a pda for a to the power n b to the power 2 n such that n is greater than or equal to 1 by final state so the set of strings accepted by this languages a double b double a four bs etc so uh the concept is we can push number of years on to the stack then for the and here we need to match 1a for two bs right so for the first b um dont do any operation on the stack no change in stack should be performed for the second b we have to pop one a from the stack right so a a b b b means two as are pushed on to the stack then for b no change in a no change in stack should be performed for the second b we have to pop one e then for the next b no change operation then for the last b next b we have to perform pop operation so now the input string is fully consumed so for the epsilon uh if the top of the stack is z naught then we can um find that the input string has n number of years followed