Constructing a PDA for the language $\{a^mb^n | m > n\}$
You can think about the scheme you proposed (push a symbol for every a, pop for every b) as using the stack as a counter. When you see an a, you increment the counter (push a symbol onto the stack) and when you see a b, you decrement the counter (pop from the stack). In the case where $m=n$, the stack should be empty after processing the whole string, or in other words the value of the counter should be 0. Following the same scheme, how would we know from the count that $m &gt; n$? What would the stack have to look like in that case?