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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. –  Alex Becker Mar 21 '12 at 3:16
    
I am sorry. I am very new to this. –  Barb Mar 21 '12 at 3:18
    
I suggest you read the 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! –  Alex Becker Mar 21 '12 at 3:19
    
Thanks Alex, I did put in the edit that I am stuck on the problem. –  Barb Mar 21 '12 at 3:22
    
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? –  Alex Becker Mar 21 '12 at 3:42

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