# Find a regular language that becomes non-regular if you cut away the middle third of all words

Let $A$ be a regular language, let $A'=\{xz\}$ such that for some $y,|x|=|y|=|z|$ and $xyz\in A$. Show that $A'$ is not necessarily regular language.

This is an excercise of Sipser, I've no idea how to construct $A,A'$ please help someone

• actually I've no idea, I showed it regular if it was "exist $|y|$ such that $|x|=|y|$ and $xy\in A$ " but no idea for this case – James Yang Aug 25 '14 at 16:50
• Please note our reference questions. In general, problems dumps such as this are problematic for SE; we don't really know what your problem is so there's little we can do to teach you fish. – Raphael Aug 26 '14 at 8:41
• L = {nonrexxxxxgular} ... – J.-E. Pin Aug 26 '14 at 10:19

Hint: Let $A = a^+ b^+ c^+$ and consider $A' \cap a^+c^+$.