# hw11 - language If “yes” then explain why If “no”...

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Spring 10: CSci 4011—Formal Languages and Automata Theory 40 points Homework 11 Out Fri., 4/23 Due Fri., 4/30 Please review the instructions given with Homework 1, as they apply to this home- work, too. Please hand in your answers to the following. Note: All Exercise/Problem/Theorem/etc. numbers correspond to the U.S. 2nd edition of the Sipser text. If you have the International edition, please check that the numbers match the ones in the U.S. edition. 1. Recall the proof of undecidability of the language E LBA (Theorem 5.10), based on computation histories. (a) Explain carefully why it is not possible to prove this result by modifying the proof of undecid- ability of E TM (Theorem 5.2), where the modi±cation consists of replacing the TM M 1 in that proof by an LBA M 1. (b) Explain carefully how the computation histories method used in the proof of Theorem 5.10 circumvents the problem identi±ed in part (a). 2. Suppose that A m B and B is a regular language. Can we conclude that A is a regular

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Unformatted text preview: language? If “yes”, then explain why? If “no”, then justify your answer with a concrete counterex-ample. 3. Prove that there exists an undecidable language that is a subset of { 1 } * . Hint: The key is to be able to encode strings from { , 1 } * using strings from { 1 } * . Develop your proof around this idea. 4. Prove that a language A is decidable if and only if A ≤ m * 1 * . (Both directions need to be proved.) 5. Let S = {a M A| M is a TM and L ( M ) = {a M A}} . Prove that neither S nor ¯ S is Turing-recognizable. Spring 10: CSci 4011—Formal Languages and Automata Theory Homework Cover Page (Please fll in and staple to the Front oF your homework) Name (print): Student ID #: Homework #: Discussion Section registered for (check one): c Sec. 2 (11:15 a.m.–12:05 p.m.; Sheng-Wen Wang) c Sec. 3 (12:20 p.m.–01:10 p.m.; Maitreyi Nanjanath) c Sec. 4 (10:10 a.m.–11:00 a.m.; Sheng-Wen Wang)...
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• Spring '08