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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 is generally considered impolite to assign the users of math.SE a homework problem.2012-03-21
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    I am sorry. I am very new to this.2012-03-21
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    I suggest you read the [faq](http://math.stackexchange.com/faq), which will help you ask better questions and get better answers. Also, it is always good to tell us what you've tried on a problem and where you're stuck. The more information we have, the better!2012-03-21
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    Thanks Alex, I did put in the edit that I am stuck on the problem.2012-03-21
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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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