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Classical and Quantum Counter Automata on Promise Problems

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Implementation and Application of Automata (CIAA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9223))

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Abstract

In this paper, we show that one-way quantum one-counter automaton with zero-error is more powerful than its probabilistic counterpart on promise problems. Then, we obtain a similar separation result between Las Vegas one-way probabilistic one-counter automaton and one-way deterministic one-counter automaton. Lastly, it was conjectured that one-way probabilistic one blind-counter automata cannot recognize Kleene closure of equality language [A. Yakaryilmaz: Superiority of one-way and realtime quantum machines. RAIRO - Theor. Inf. and Applic. 46(4): 615–641 (2012)]. We show that this conjecture is false.

M. Nakanishi—Partially supported by JSPS KAKENHI Grant Numbers 24500003 and 24106009, and also by the Asahi Glass Foundation.

A. Yakaryılmaz—Partially supported by CAPES with grant 88881.030338/2013-01.

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Notes

  1. 1.

    The input is read as a stream from left to right and a single symbol is fed to the machine in each step. We also use two end-markers to allow the machine making some pre- and post-processing.

  2. 2.

    The input is written on a single-head read-only tape between two end-markers and the head can move in both directions or stay in the same tape square in each step.

  3. 3.

    It is a restricted version of two-wayness such that the head cannot move to the left.

  4. 4.

    A single answer is given with probability 1.

  5. 5.

    A classical reversible operation defined on the set of configurations is a unitary operator containing only 0 s and 1s.

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Acknowledgement

We thank Klaus Reinhardt for answering our question regarding the subject matter of this paper.

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Authors and Affiliations

  1. Faculty of Education, Art and Science, Yamagata University, Yamagata, 990-8560, Japan

    Masaki Nakanishi

  2. National Laboratory for Scientific Computing, Petrópolis, Rj, 25651-075, Brazil

    Abuzer Yakaryılmaz

Authors
  1. Masaki Nakanishi
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  2. Abuzer Yakaryılmaz
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Correspondence to Masaki Nakanishi .

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Editors and Affiliations

  1. Umeå University, Umeå, Sweden

    Frank Drewes

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Nakanishi, M., Yakaryılmaz, A. (2015). Classical and Quantum Counter Automata on Promise Problems. In: Drewes, F. (eds) Implementation and Application of Automata. CIAA 2015. Lecture Notes in Computer Science(), vol 9223. Springer, Cham. https://doi.org/10.1007/978-3-319-22360-5_19

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  • DOI: https://doi.org/10.1007/978-3-319-22360-5_19

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