下推自动机和算术表达式

Question

I am trying to figure out how to do arithmetic expressions in Pushdown Automata ?(PDA) for example L=W|W=An Bm Cn-m What i am thinking of doing is to push As then pop Bs and then either pop As with C or Bs with C depending what is left. For example aaabbc (pushing aaa then popping with Bs bba and then either pop A with C or B with C depending which one is bigger.

Answer 1

For a word w to be in the language, it has to have n>=m by your definition (otherwise C^(nm) is negative, and that's impossible).

So, your automaton basically needs to:

1. Push to stack when seeing 'a'
2. pop from stack upon seeing 'b'
3. pop from stack upon seeing 'c'.

Also, some important issues:

• You need to move between different states when seeing a 'new' character.
• Your automaton should accept w=eps (empty word).
• w=a^bb^n is also in the language, make sure you take care of that.

I hope I gave you good enough leads to solve it on your own..

Good luck!