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Unformatted text preview: CSE 105: Automata and Computability Theory Winter 2012 Problem Set #2
Due: Friday, February 10th, 2012 Problem 1 For a string x, let xR denote the symbolbysymbol reverse of x. In other words, if x = x1 x2 . . . xn then xR = xn xn1 . . . x1 . For a language L, let LR denote xR x L . Prove that if L is regular then so is LR . Hint: Given a DFA M accepting L construct an NFA M R accepting LR . Problem 2 Suppose that L1 and L2 are nonregular languages over some alphabet . Is L1 L2 always nonregular? Is L1 L2 always nonregular? Explain. Problem 3 Consider the language of palindromes over = {0, 1}. (Palindromes are strings that remain the same if reversed. For example, "bob" or, ignoring spaces, "lisa bonet ate no basil".) Using the characterbycharacter operator wR introduced in Problem 1, above, we can write Lbob = {w  w = wR }. a. Prove that the language Lbob is not regular. b. Give a contextfree grammar whose language is Lbob . Problem 4 Let L1 be a regular language and L2 be a contextfree language over some alphabet . Show that L1 L2 is contextfree. Hint: You'll want to work with PDAs here, not CFGs. 1 ...
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 Winter '99
 Paturi

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