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--- lfa:2022:lab08-the-pumping-lemma [2022/11/28 12:10]
mihai.udubasa
+++ lfa:2022:lab08-the-pumping-lemma [2022/12/09 08:55] (current)
pdmatei
@@ Line 18: / Line 18: @@
 **8.1.1.** Show that the pumping lemma holds for finite languages.
-/*
 <hidden Solution>
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 </hidden>
-*/
 **8.1.2.*** Find a language which is not regular for which the pumping lemma holds.
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 **8.2.1.** $  L = \{ \: A^n B^m \: | \: 0 \leq n \leq m \: \} $
-/*
 <hidden Solution> <note>
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 </hidden>
-*/
-**8.2.2.** $  L = \{ \: w \in \{A,B\}^* \: | \: \#A(w) = \#B(w) \: \} $
-/*
+**8.2.2.** $  L = \{ \: w \in \{A,B\}^* \: | \: \#_A(w) = \#_B(w) \: \} $
 <hidden Solution> <note>
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 </hidden>
-*/
 **8.2.3.** $math[L = \{(01)^n(10)^n \mid n > 0 \} ]
-/*
 <hidden Solution> <note>
 $ w_n = (01)^n(10)^n $
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 </hidden>
-*/
 **8.2.4.** $  L = \{ \: w \in \{A,B\}^* \: | \: \text{w is a palindrome} \: \} $
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 <hidden Solution> <note>
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 </hidden>
-*/
 **8.2.5.** $  L = \{ \: w \in \{0\}^* \: | \: \text{the length of w is a prime number} \: \} $
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 <hidden Solution> <note>
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 </hidden>
-*/
 **8.2.6.** $  L = \{ \: w \in \{0\}^* \: | \: \text{the length of w is a power of two} \: \} $
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 <hidden Solution> <note>
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 </hidden>
-*/
 **8.2.7.** $  L = \{ \: ww^R  \: | \: w\in \{0,1\}^* \} $
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 <hidden Solution> <note>
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 </hidden>
-*/
 ===== 8.3. Combining the pumping lemma with closure properties =====
 **8.3.1.** Using the pumping lemma, prove that $  L = \{ \: A^nB^m \: | \: n \neq m \}$ is not a regular language.
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 <hidden Solution>
 <note>
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 </hidden>
-*/
 /*
 ====== Homework ======