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# hw10 - Spring 10 CSci 4011Formal Languages and Automata...

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Spring 10: CSci 4011—Formal Languages and Automata Theory 40 points Homework 10 Out Fri., 4/16 Due Fri., 4/23 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. The presence of a hint in a problem does not necessarily mean that it is hard. It is merely to get you started in the correct direction. 1. Let S = {a M A | M is a DFA and M accepts w R whenever it accepts w } . (Here w R is the rever- sal of string w .) Prove that S is decidable. Hint: Use one of the deciders for regular languages from Sec. 4.1 as a subroutine in your decider for S . You will also ±nd the result of Problem 6 in Homework 2 useful. (You may use this also as a subroutine, without rewriting it.)

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• Spring '08