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Fix an alphabet ${\bf S}$ and a language $L \subset S^*$. For any two words $w$, w' $\in S^*$, define a relation w \sim w' if and only if Cone$(w)$ = Cone$(w')$. Then prove that this is an equivalence relation on $s^*$ and rephrase the Myhill - Nerode Theorem in terms of this equivalence relation. I am stuck on the problem. I do not have an idea how to start.

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    It would be helpful if you told us what you do know about the problem. Do you know what it's asking? Are you familiar with the terms?2012-03-21

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