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Decidable and undecidable problems about quantum automata

Vincent D. Blondel·Emmanuel Jeandel·Pascal Koiran·Natacha Portier
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Abstract

We study the following decision problem: is the language recognized by a quantum finite automaton empty or non-empty? We prove that this problem is decidable or undecidable depending on whether recognition is defined by strict or non-strict thresholds. This result is in contrast with the corresponding situation for probabilistic finite automata for which it is known that strict and non-strict thresholds both lead to undecidable problems.

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Vincent D. Blondel, Emmanuel Jeandel, Pascal Koiran, Natacha Portier. 2003-04-11. Decidable and undecidable problems about quantum automata. https://arxiv.org/abs/quant-ph/0304082

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