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Let $x,y,z,w$ be finite strings. Find the necessary and sufficient conditions for the following two equations to hold simultaneously: $$xy=zw$$ and $$yx=wz$$ Automata Theory is new to me and i am struggling with this problem given in my tutorial sheet.Help me.Thanks in advance.

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    Obviously, it is sufficient that $x=z$ and $y=w$.2012-07-05

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