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.
Categories: cs.FL cs.LO