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Unformatted text preview: ∈ L and w ∈ LL } Prove that if L is a regular language, then F ( L ) is also regular. 71 Problem 5 (optional) An allNFA is a 5tuple ( Q, Σ ,δ,q ,F ) that operates exactly as an NFA does with one crucial diﬀerence: an allNFA will accept a string w if every valid computation on w ends in an accepting state. (By contrast, an ordinary NFA will accept a string w if there exists a valid computation on w that ends in an accepting state.) Prove that the class of languages accepted by allNFAs is the class of regular languages. Problem 6 (optional) If L is a language, let L 1 2be the set of all ﬁrst halves of strings in L . That is, L 1 2= { x 5 y :  x  =  y  and xy ∈ L } . Prove that if L is regular, L 1 2is also regular. 72...
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 Spring '10
 Mr.ElieNasr

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