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Problem 1 (35 points): Let L be a regular language over some alphabet . Prove that the following language is also regular: For example, if

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Problem 1 (35 points): Let L be a regular language over some alphabet . Prove that the following language is also regular: For example, if the language L over -{0, 1, 2} contains 0121 then L Optional hint: Since L is a regular language, there is a DFA M for L. Using M, think about constructing a new DFA Mstrange for Lstrange by processing input symbols in pairs. strage contains 1012

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