l17-handout

l17-handout - Outline Push Down Automata introduction...

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Pumping Lemma David Dill Department of Computer Science 1 Outline Push Down Automata introduction Language of a PDA Acceptance by final state vs. empty stack Equivalence of CFGs and PDAs Context-free pumping lemma. 2 PDA Formalities ( Q, Σ , Γ , δ, q 0 , Z 0 , F ) Γ is the stack alphabet . Z 0 is the start symbol . PDA starts with Z 0 on the stack and nothing else. δ : Q × ² ) × Γ 2 Q × Γ * (The value of δ must be a finite set, though.) δ bases possible next configuration on: the current state, the input (or ² ), and the top symbol on the stack. It gets a set of non-deterministic choices, each of which specifies the next state and a string of new symbols to be pushed on the stack Everything else is as in an e-NFA 3 Acceptance by a PDA An instantaneous description is a snapshot of the PDA: Def An instantaneous description of a PDA is The current state. The complete contents of the stack. The input that has not yet been read. So an ID has the type Q × Σ * × Γ * . E.g., ( q, w, α ) , where q is the current state, w is the unread input, and α is the stack (with the top symbol first). The ID has everything necessary to predict the possible future IDs of the PDA.
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l17-handout - Outline Push Down Automata introduction...

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