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flac-hw1

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Name: FLAC Assignment 1 Please read all questions ASAP. If a question is unclear, please email the TAs. Clarifications may also be posted on the Assignments page of the course website. Remember to staple together all pages of your com- pleted assignment. Exercise 1.1. To the right are the state diagrams of two DFAs, M 1 and M 2 . Answer the following questions about these machines. a. What is the start state of M 1 ? b. What is the set of accepting states of M 1 ? c. What is the start state of M 2 ? d. What is the set of accepting states of M 2 ? e. What sequence of states does M 1 go through on input aabb ? f. Does M 1 accept the string aabb ? g. Does M 2 accept the empty string Λ? Exercise 1.4. Give state diagrams of DFAs recognizing the following languages. In all cases, the alphabet is { 0 , 1 } . a. { w | w begins with a 1 and ends with a 0 } . b. { w | w contains at least three 1s } . c. { w | w contains the substring 0101, i.e., w = x 0101 y for some (possibly empty) x and y } .

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