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## Homework Statement

"Let L be any regular language over an alphabet Σ. Using L, we define

chop(L) = {w : ∃ x, y, z ∈ Σ∗ , xyz ∈ L, w = xz}.

Show that chop(L) is regular or give a counter-example."

## Homework Equations

If an NFA that describes the language chop(L) exists, then chop(L) is a regular language.

## The Attempt at a Solution

I'm trying to make a non-deterministic finite automaton (NFA), since if one can be made, then I believe that that proves that the language is regular.

Here ( https://www.docdroid.net/ZVsWIlb/nfa.pdf ) is my attempt at making such an NFA. Is that correct? If not, what's wrong with it?

Any input would be greatly appreciated!

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