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Unformatted text preview: CS 154 Intro. to Automata and Complexity Theory Handout 8 Autumn 2009 David Dill October 8, 2009 Solution Set 1 Problem 1 (a) The desired DFA is given as follows: q4 Start 1 1 0,1 1 1 q0 q1 q2 q3 (b) The desired DFA is given as follows: q2 1 1 1 1 Start q3 q0 q1 Comment: One common mistake is forgetting to specify some of the transitions. Another is to incorrectly define some transitions. Hint: try to check that your automaton does not accept anything not in the language or reject anything in the language. Problem 2 (a) The desired NFA is given as follows: Comment: A common mistake is to add too many transitions to the NFA, such as a transition on from any of q 2 , . . . , q 5 back to q 2 . Another common mistake is to add the transition on 1 from q 6 to q 1 instead of q 2 . 1 q0 Start 0,1 0,1 0,1 0,1 0,1 0,1 1 0,1 q4 q7 q6 q5 q3 q2 q1 (b) Suppose that the DFA has less than 2 5 states. Then (by the pigeon- hole principle) there exists a state q that two distinct strings of length 5 will reach. That is, there are two strings5 will reach....
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