lect11-pda1 - PushdownAutomata Definition MovesofthePDA...

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1 Pushdown Automata Definition Moves of the PDA Languages of the PDA Deterministic PDA’s
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2 Pushdown Automata The PDA is an automaton equivalent to  the CFG in language-defining power. Only the nondeterministic PDA defines all  the CFL’s. But the deterministic version models  parsers. Most programming languages have  deterministic PDA’s.
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3 Intuition : PDA Think of an  ε -NFA with the additional  power that it can manipulate a stack. Its moves are determined by: 1. The current state (of its “NFA”), 2. The current input symbol (or  ε ), and  3. The current symbol on top of its stack.
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4 Intuition : PDA – (2) Being nondeterministic, the PDA can  have a choice of next moves. In each choice, the PDA can: 1. Change state, and also 2. Replace the top symbol on the stack by a  sequence of zero or more symbols. Zero symbols = “pop.” Many symbols = sequence of “pushes.”
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5 PDA Formalism A PDA is described by: 1. A finite set of  states   (Q, typically). 2. An  input alphabet   ( Σ , typically). 3. stack alphabet   ( Γ , typically). 4. transition function   ( δ , typically). 5. start state   (q 0 , in Q, typically). 6. start symbol   (Z 0 , in  Γ , typically). 7. A set of  final states   (F    Q, typically).
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6 Conventions a, b, … are input symbols. But sometimes we allow  ε  as a possible  value. …, X, Y, Z are stack symbols. …, w, x, y, z are strings of input  symbols. α β ,… are strings of stack symbols.
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7 The Transition Function Takes three arguments: 1. A state, in Q. 2. An input, which is either a symbol in  Σ  or  ε . 3. A stack symbol in  Γ . δ (q, a, Z) is a set of zero or more  actions  of the form (p,  α ).
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