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I've been trying to find a super simple explanation of Push-Down Automaton. This is what I've come up with so far:

  1. A PDA has three operations:

    • A push to the stack; given an input state, input symbol, and the top stack symbol
    • A pop from the stack; given an input state, input symbol, and the top stack symbol
    • A "switch" operation, replacing the top of the stack with another symbol; given an input state, input symbol, and the top stack symbol

  2. A PDA has two accepting forms:

    • Operations such that the stack has been emptied
    • Operations such that the stack is back to the starting symbol, and on an accepted final state.

I'm wondering if my second point here is correct. Are these the only two ways a PDA will accept a string, and are these even correct? I've found a ton of examples, but no super simple explanation of the idea.

user3470131
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  • Fully answering this question would require [a textbook](http://www.amazon.ca/Introduction-Automata-Languages-Computation-Edition/dp/0321455363). For example, your third operation is a special case of your first two. The first clause of your second “accepting forms” is merely a special case of the second clause, and the entire second “form” is a special case of your first form. – Dour High Arch Dec 01 '14 at 19:11
  • A PDA accepts input when the stack contains only the bottom symbol (it is empty) and the input sequence consists of the end ($) symbol (it is exhausted). I don't understand your question. – Apalala Dec 02 '14 at 22:46

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