Let $L$ be a regular language. I need to prove that the language $M_L = \{w \in L \; | \forall x \in L \; \forall y \in \Sigma^+ : w \neq xy \}$ that contains all words of L that do not have a related proper prefix in L is regular.
As an example I thought about the language $L_1 = \{12,34,56,3456\}$ where $M_{L_1} = \{12,34,56\}$. I played around with complement of the automaton of the language L and the intersection of this automaton with the one of the language L (no complement) and some modifications, but am stuck right now.
Could you please help me to go on?
Thanks in advance!