Unformatted text preview: that the class of languages recognized by NFAs is not closed under complement? 3. Using the Pumping Lemma, prove that following languages are not regular: (a) L = { n 1 m  m,n ≥ 0 and m leaves a remainder of 3 when divided by n . } (b) L 1 = { n 1 m  n,m ≥ 0 and n 6 = m } . (c) L 2 = { w  w ∈ { , 1 } * and w is not a palindrome } . 4. Let CFG G be: S → aSb  Y b  Y a Y → bY  aY  ± Prove that L ( G ) = { a,b } + . 5. For a language L , let Init ( L ) = { x  xy ∈ L for some y ∈ Σ * } . Let r , s , r I and s I be regular expressions for the languages R , S , Init ( R ), and Init ( S ) respectively. Using only these regular expressions and the operations +, concatenation, and * , give expressions for the following languages and brieﬂy justify your answers (Be careful! Contemplate your answers.): (a) (3 points) Init ( R ∪ S ). (b) (3 points) Init ( RS ) . (c) (3 points) Init ( R * ). 1...
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 Spring '10
 FarzanAzadeh
 Formal language, Formal languages, Regular language, Contextfree grammar, contextfree language

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