Two-way Quantum One-counter Automata
<|reference_start|>Two-way Quantum One-counter Automata: After the first treatments of quantum finite state automata by Moore and Crutchfield and by Kondacs and Watrous, a number of papers study the power of quantum finite state automata and their variants. This paper introduces a model of two-way quantum one-counter automata (2Q1CAs), combining the model of two-way quantum finite state automata (2QFAs) by Kondacs and Watrous and the model of one-way quantum one-counter automata (1Q1CAs) by Kravtsev. We give the definition of 2Q1CAs with well-formedness conditions. It is proved that 2Q1CAs are at least as powerful as classical two-way deterministic one-counter automata (2D1CAs), that is, every language L recognizable by 2D1CAs is recognized by 2Q1CAs with no error. It is also shown that several non-context-free languages including {a^n b^{n^2}} and {a^n b^{2^n}} are recognizable by 2Q1CAs with bounded error.<|reference_end|>
@article{yamasaki2001two-way,
    title={Two-way Quantum One-counter Automata},
    author={Tomohiro Yamasaki, Hirotada Kobayashi, Hiroshi Imai},
    journal={arXiv preprint arXiv:cs/0110005},
    year={2001},
    archivePrefix={arXiv},
    eprint={cs/0110005},
    primaryClass={cs.CC quant-ph}
}