Let L>λ​(A) and L≥λ​(A) be the
languages recognized by {\em measure many 1-way quantum finite automata
(MMQFA)} (or,{\em enhanced 1-way quantum finite automata(EQFA)}) A
with strict, resp. non-strict cut-point λ. We consider the languages
equivalence problem, showing that
\begin{itemize}
\item {both strict and non-strict languages equivalence are undecidable;}
\item {to do this, we provide an additional proof of the undecidability of
non-strict and strict emptiness of MMQFA(EQFA), and then reducing the languages
equivalence problem to emptiness problem;}
\item{Finally, some other Propositions derived from the above results are
collected.}
\end{itemize}Comment: Readability improved, title change