construct a deterministic PDA for the language

Question

Can someone help me to construct a deterministic PDA for the following language:

$L = \{0^n1^m | n \geq m$ and $m,n \geq 0 \}$

Here is my suggestion : the states are z0,z1,z2 , z0 is final state , for the empty string , z1 should also be finate state :

Answer 1

Since you are confused, here are four hints to get you going. You will still have to think through the machine, but here are some of the big pieces:

1. Push a marker onto the stack that will tell you where the bottom of the stack is. (Let's say, $\$$)
2. Every time you find an $0$, push a symbol (let's say, $p$) onto the stack.
3. When you finally find an $1$, stop pushing. Start popping off $p$s.
4. If you reach the $\$$ before you've reached the end of your $1$s, then you've broken the $n \geq m$ condition.