Languages Recognized with Unbounded Error by Quantum Finite Automata

We prove the following facts about the language recognition power of Kondacs-Watrous quantum finite automata in the unbounded error setting: One-way automata of this kind recognize all and only the stochastic languages. When the tape head is allowed two-way (or even "1.5-way") movement, more languages become recognizable. This leads to the conclusion that quantum Turing machines are more powerful than probabilistic Turing machines when restricted to constant space bounds.

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