Computational language theory proof

sbc824
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Homework Statement



I need to prove this

http://www.freeimagehosting.net/newuploads/66exd.jpg

R represents the reversal of...L1 and L2 represent languages, which can represent strings.

(L1L2) = the concatenation of L1 and L2

Ex.

L1 = 01001
L2 = 001

L1L2 = 01001001
(L1L2)^R = 10010010


The Attempt at a Solution



Let y be a member of E* denote an arbitrary string in the set (L1L2)^R.

This is where I'm stuck...
 
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sbc824 said:

Homework Statement



I need to prove this

http://www.freeimagehosting.net/newuploads/66exd.jpg

R represents the reversal of...L1 and L2 represent languages, which can represent strings.

(L1L2) = the concatenation of L1 and L2

Ex.

L1 = 01001
L2 = 001

L1L2 = 01001001
(L1L2)^R = 10010010
And what is L2^RL1^R? That seems the obvious thing to calculate to see what the question is asking.

The Attempt at a Solution



Let y be a member of E* denote an arbitrary string in the set (L1L2)^R.

This is where I'm stuck...
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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