Chapter2Section2_F11

Chapter2Section2_F11 - 91.304 Foundations of (Theoretical)...

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91.304 Foundations of (Theoretical) Computer Science Chapter 2 Lecture Notes (Section 2.2: Pushdown Automata) Prof. Karen Daniels, Fall 2011 , with acknowledgement to: - ipser troduction to the Theory of Computation xtbook Sipser Introduction to the Theory of Computation textbook and - Dr. David Martin 1
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Overview ew computational model: ± New computational model: ² Pushdown Automata (like NFA, but add a stack) ± Definition, Examples ,p ± Equivalence with Context-Free Grammars ² Theorem 2.20: A language is context-free iff some pushdown automaton recognizes it. ² Lemma 2.21 ( ) If a language is context-free, then some pushdown automaton recognizes it. ² Lemma 2.27 ( ) If a pushdown automaton recognizes some language, then it is context-free. 2
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Pushdown Automata Definition ± Like NFA, but add a stack states and transition function stack can hold unlimited amount of information 3 Source: Sipser Textbook
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Pushdown Automata Definition ± Formal Definition (6-tuple uses nondeterminism) : Nondeterministic PDA’s are more powerful than deterministic ones. We focus on nondeterministic ones because they are as powerful as context-free grammars. } { ε Γ = Γ 4 Source: Sipser Textbook
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Pushdown Automata Definition ± Formal Definition: Specification of F , δ 5 Source: Sipser Textbook
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Pushdown Automata Examples $ for empty stack test not regular! 6 Source: Sipser Textbook a,b c means: when machine is reading a from input, it replaces b (from top of stack) with c .
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Pushdown Automata Examples xample 2 16 ± Example 2.16 Nondeterministically guess whether to match i = j or i = k . $ for empty stack test 7 Source: Sipser Textbook a,b c means: when machine is reading a from input, it replaces b (from top of stack) with c .
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Pushdown Automata Examples ± Example 2.18 $ for empty stack test Nondeterministically guess end of w . 8 Source: Sipser Textbook a,b c means: when machine is reading a from input, it replaces b (from top of stack) with c .
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Equivalence with Context-Free Grammars ± Theorem 2.20 : A language is context-free iff ome pushdown automaton recognizes it some pushdown automaton recognizes it.
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This note was uploaded on 02/13/2012 for the course CS 91.304 taught by Professor Staff during the Fall '11 term at UMass Lowell.

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Chapter2Section2_F11 - 91.304 Foundations of (Theoretical)...

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