# hw3 - your construction and give the formal speci²cation...

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Spring 10: CSci 4011—Formal Languages and Automata Theory 40 points Homework 3 Out Fri., 2/5 Due Fri., 2/12 Please review the instructions given with Homework 1, as they apply to this home- work, too. Please hand in your answers to the following: 1. Give the regular expression for each of the regular languages below. In each case, let Σ = { 0 , 1 } . (a) { w Σ * | w contains an even number of 0’s or two 1’s } (b) { w Σ * | w does not contain the substring 11 } 2. Ex. 1.19(a), p. 86. Show intermediate steps. 3. Ex. 1.21(b), p. 86. Show intermediate steps. 4. Ex. 1.25, p. 87. 5. Ex. 1.27, p. 88. 6. Ex. 1.40(b), p. 89. Give an NFA for NOEXTEND ( A ). Describe brie±y the idea behind your construction and give the formal speci²cation of the machine. 7. Ex. 1.41, p. 89. Give a DFA for the perfect shu³e of A and B . Describe brie±y the idea behind

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Unformatted text preview: your construction and give the formal speci²cation of the machine. Hint: DFA M (for the perfect shu³e) simulates DFAs M 1 (for A ) and M 2 (for B ) alternately. States of M will be of the form ( q 1 ,q 2 ,t ), where q 1 ∈ M 1 , q 2 ∈ M 2 , and t ∈ { 1 , 2 } indicates which of M 1 and M 2 is being simulated currently. 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