  Let $L_{>\lambda}(\mathcal{A})$ and $L_{\geq\lambda}(\mathcal{A})$ be the
languages recognized by {\em measure many 1-way quantum finite automata
(MM-QFA)} (or,{\em enhanced 1-way quantum finite automata(EQFA)}) $\mathcal{A}$
with strict and non-strict cut-point $\lambda$, respectively. We consider the
language equivalence problem and show the following
  1. both strict and non-strict language equivalence are undecidable;
  2. we provide an another proof of the undecidability of non-strict and strict
emptiness of MM-QFA and EQFA, and then reducing the language equivalence
problem to emptiness problem;
  3. lastly, we obtain some other properties which can be derived from the
above results.

Formal Languages and Automata Theory;Logic in Computer Science