When Context Free is actually Regular

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Homework Statement



What is an algorithm which decides whether a context-free language is actually a subset of a regular language? That is, given CFL and RL, how do we decide whether CFL is a subset of RL?
 
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I do not understand. You want to decide if context free language s a subset of any regular language? It always happens. If L is CFL over alphabet A, then A* is regular and L is subset of A*.
 
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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