pumping Lemma - S tandard Re se pre ntations of Re gular...

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Fall 2004-2005 CSI 301 1 Standard Representations of Regular Languages Regular Languages DFAs NFAs Regular Expressions Grammars
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Fall 2004-2005 CSI 301 2 When we say: We are given a Regular Language We mean: L Language is in a standard representation L
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Fall 2004-2005 CSI 301 3 Elementary Questions about Regular Languages
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Fall 2004-2005 CSI 301 4 Membership Question Question: Given regular language and string how can we check if ? L L w w Answer: Take the DFA that accepts and check if is accepted L w
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CSI 301 5 DFA L w L w w w
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Fall 2004-2005 CSI 301 6 Given regular language how can we check if is empty: ? L L Take the DFA that accepts Check if there is any path from the initial state to a final state L ) ( = L Question: Answer:
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CSI 301 7 DFA L = L
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Fall 2004-2005 CSI 301 8 Given regular language how can we check if is finite? L L Take the DFA that accepts Check if there is a walk with cycle from the initial state to a final state L Question: Answer:
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Fall 2004-2005 CSI 301 9 DFA L is infinite L is finite
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Fall 2004-2005 CSI 301 10 Given regular languages and how can we check if ? 1 L 2 L 2 1 L L = Question: = ) ( ) ( 2 1 2 1 L L L L Find if Answer:
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Fall 2004-2005 CSI 301 11 = ) ( ) ( 2 1 2 1 L L L L = 2 1 L L = 2 1 L L and 2 1 L L = 1 L 2 L 1 L 2 L 2 1 L L 1 2 L L 2 L 1 L
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Fall 2004-2005 CSI 301 12
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pumping Lemma - S tandard Re se pre ntations of Re gular...

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