CT-review - Review Elements of Computation Theory XIAOGANG...

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Review: Elements of Computation Theory XIAOGANG JIN AI Institute, College of Computer Science Zhejiang University E-Mail: [email protected] () 1 / 24
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1 Regular Language 2 Context-free Language(CFL) 3 Turing Machine and Recursive Enumerable Language 4 Undecidablity 5 P and NP Problems 6 NP- Complete Problems () 2 / 24
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Outline 1 Regular Language 2 Context-free Language(CFL) 3 Turing Machine and Recursive Enumerable Language 4 Undecidablity 5 P and NP Problems 6 NP- Complete Problems () 3 / 24
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Regular Language Regular Expression Deterministic finite automata(DFA) Non-deterministic finite automata(NFA) Closure properties and Pumping Theorem State Minimization (graduated course) () 4 / 24
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Regular Language Regular Expression Deterministic finite automata(DFA) Non-deterministic finite automata(NFA) Closure properties and Pumping Theorem State Minimization (graduated course) Question: Give a DFA or NFA Regular Expression (Example 2.3.2 P 81); Give a Regular Expression DFA or NFA (Theorem 2.3.1 P 75); Show a given language be regular or non-regular? (Yes, regular expression, DFA, NFA and closure property; No, Pumping theorem or closure property) () 4 / 24
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Regular Language 2.4.8 Are the following statements true od false? Explain you answer in each case. (P 91) Every subset of a regular language is regular. ( F ) Every regular language has a regular proper subset. ( F ) (Hint: ) If L is regular, then so is { xy | x L and y L } . ( T ) (Hint: { xy | x L and y L } = L ¯ L ) { w | w = w R } is regular. ( F ) If L is regular, then so is { w | w L and w R L } . ( T ) (Hint: L = L L R .) If C is any set of regular languages, then C is a regular language. ( F ) { xyx R | x , y Σ * } is regular. ( T ) (Hint: { xyx R | x , y Σ * } = Σ * . By letting x = e , y can vary over all the strings of Σ * .) () 5 / 24
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Outline 1 Regular Language 2 Context-free Language(CFL) 3 Turing Machine and Recursive Enumerable Language 4 Undecidablity 5 P and NP Problems 6 NP- Complete Problems () 6 / 24
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Context-free Language Context-free Grammar(CFG) Pushdown automata Closure properties and Pumping Theorem () 7 / 24
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Context-free Language Context-free Grammar(CFG) Pushdown automata Closure properties and Pumping Theorem Question: Give a context-free language
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