PDA to accept a language of strings containing more a's than b's

Question

Produce a PDA to recognise the following language : the language of strings containing more a\'s than b\'s

I have been struggling with this

Answer 1

I have come up with a more general solution to the problem concerning the number of as and bs, see the picture below:

where a > b means more as than bs and so does a < b , a = b.

Z means the bottom of stack, and A/B are stack symbols.

I'm excited about it because this PDA seperates the 3 different states. In your problem, you can just set the a > b state to be the final state and let a = b be the start state.

And if you want to step further, you can use this PDA to easily generate PDAs for a >= b, a - b >= 1, 2 <= a - b <= 3 etc, which is fascinating.