# hw9 - Ch 0 You may give your answer descriptively in plain...

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Spring 10: CSci 4011—Formal Languages and Automata Theory 40 points Homework 9 Out Fri., 4/9 Due Fri., 4/16 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. Ex. 3.11, p. 161. Answer this question by showing how an ordinary TM can simulate a TM with doubly-in±nite tape and vice versa. You may give your answer descriptively, in plain English, but be sure that the main ideas come through clearly. Hint: Recall that an ordinary TM is equivalent to a multi-tape TM, so consider using the latter in your simulation. 2. Prove that an in±nite language is decidable if and only if some enumerator enumerates the language in lexicographic order. (Use the de±nition of “lexicographic order” given on p. 14 of

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Unformatted text preview: Ch. 0.) You may give your answer descriptively, in plain English, but be sure that the main ideas come through clearly. 3. Let A LL DFA = {a A A| A is a DFA and L ( A ) = Σ * } . Prove that A LL DFA is decidable. 4. Let A ε CFG = {a G A| G is a CFG that generates ε } . Prove that A ε CFG is decidable. 5. Let A = {a R,S A| R and S are regular expressions and L ( R ) ⊆ L ( S ) } . Prove that A is decid-able. 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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## This note was uploaded on 10/21/2011 for the course CSCI 4011 taught by Professor Nadathur during the Spring '08 term at Minnesota.

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hw9 - Ch 0 You may give your answer descriptively in plain...

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