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Can anyone give an example of two non-regular languages $A, B \subseteq \{0, 1\}^∗$ for which the language $AB$ is regular?

Rick Decker
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David
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1 Answers1

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Hint: Let $C$ be the language of words that have the same number of 1's as 0's. Is $C$ regular? Let $A = \{0,1\}^* \setminus C$. Is $A$ regular? Now, can you find a non-regular language $B$ that will make $AB$ regular?

D.W.
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