lect11-pda1

lect11-pda1 - 1 Pushdown Automata Definition Moves of the...

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Unformatted text preview: 1 Pushdown Automata Definition Moves of the PDA Languages of the PDA Deterministic PDA’s 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. 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. 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.” 5 PDA Formalism ◆ A PDA is described by: 1. A finite set of states (Q, typically). 2. An input alphabet ( Σ , typically). 3. A stack alphabet ( Γ , typically). 4. A transition function ( δ , typically). 5. A start state (q , in Q, typically). 6. A start symbol (Z , in Γ , typically). 7. A set of final states (F ⊆ Q, typically). 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. 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 ....
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This note was uploaded on 03/30/2012 for the course CS 154 taught by Professor Motwani,r during the Spring '08 term at Stanford.

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lect11-pda1 - 1 Pushdown Automata Definition Moves of the...

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