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I think I know the pumping lemma and was told that Myhill-Nerode is a very elegant way to show that something is regular or not regular. But I am having a lot of trouble with it. Take this for example:

L = {0k, k = 2n, n >̲ 1}

My language is the repetition of 0 to a length that's a power of 2. I want to use the Myhill-Nerode to show that this is either regular or not regular. Is it possible?

I know how to set this up to resemble other Myhill-Nerode looking proofs but I don't understand the equivalence concept that much.

I could say that I have some j and p where j ≠ p and both are of the form 2h and h e N, I then define a, b and c so that:

a = 0j/2

b = 0p/2

c = 0j/2

Where ac = 0j/20j/2 = 0j is in my language since j is of the form 2n, however bc = 0p/20j/2 is not guaranteed to be in my language for every p and j, since j ≠ p

David Zorychta
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1 Answers1

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Given a languages L, two strings u, v 2 L are equivalent if for all strings w belong to sigma * we have that u.w belongs to L iff v.w belongs to L

consider the set of {0,0^2,0^4,0^8....}, in this case for some m and n 0^m and 0^n should be mapped to the same equivalence class or else there would be infinite equivalence classes making it non-regular by Myhill-Nerode theorem. However 0^m.0^m belong to L but 0^n.0^m would not ..Hence

Aditya Nambiar
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