Undecidability of MM-QFAs Language Equivalence Problem

Tianrong Lin

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arXiv · 1308.3301

Undecidability of MM-QFAs Language Equivalence Problem

Tianrong Lin

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Abstract

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.

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Tianrong Lin. 2013-08-15. Undecidability of MM-QFAs Language Equivalence Problem. https://arxiv.org/abs/1308.3301

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