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Unformatted text preview: b , c } in which the total number of b ’s and c ’s is three. 4. Let L be the language over { a , b } generated by the recursive definition: i) Basis: λ∈ L ii) Recursive step: If u ∈ L then aaub ∈ L iii) Closure: A string w is in L only if it can be obtained from the Basis by finite number applications of the Recursive step. Prove by induction that for any u ∈ L the number of a ’s in u is twice the number of b ’s. 5. Prove or disprove that if X * = Y * , then X = Y. 6 Write down the transition function for the following DFA: 7. Construct the DFA to recognize the language of all strings over { a , b } in which the number of a ’s is divisible by 3. Give the diagram and transition table. b b b b a a a a 1 2 3...
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 Spring '09
 Natural number, Regular expression

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