# sfake3do1 - 6.045J/18.400J Automata Computability and...

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Unformatted text preview: 6.045J/18.400J: Automata, Computability and Complexity Prof. Nancy Lynch Homework FAKE 3.1: Solutions Due: NEVER Elena Grigorescu Problem 1 : Algorithms for finite automata (From Sipser Problem 4.11) Design: (a) An algorithm that determines, for any DFA M with alphabet { , 1 } , whether or not M accepts any string containing an odd number of 1s. (b) An algorithm that determines for any DFA M with alphabet { , 1 } , whether or not M accepts all strings containing an odd number of 1s. Solution 1.a: 1. Create a DFA D for { w ∈ { , 1 } * | w contains an odd number of 1s } . 2. Use the product construction to create a DFA T recognizing L ( M ) ∩ L ( D ) (i.e., all strings in L ( M ) that contain an odd number of 1s). 3. Run E DFA (Theorem 4.4 on page 168 of Sipser) to test if T recognizes the empty language, and return the opposite of what E DFA returns. Solution 1.b: 1. Create a DFA D for { w ∈ { , 1 } * | w contains an odd number of 1s } ....
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sfake3do1 - 6.045J/18.400J Automata Computability and...

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