Skip to main content
SpringerLink
Log in

Languages Recognized with Unbounded Error by Quantum Finite Automata

  • Conference paper
Computer Science - Theory and Applications (CSR 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5675))

Included in the following conference series:

Abstract

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.

This work was partially supported by the Bog̃aziçi University Research Fund with grant 08A102 and by the Scientific and Technological Research Council of Turkey (TÜBİTAK) with grant 108E142.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ablayev, F.M., Gainutdinova, A.: Classical simulation complexity of quantum machines. In: Lingas, A., Nilsson, B.J. (eds.) FCT 2003. LNCS, vol. 2751, pp. 296–302. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  2. Adleman, L.M., DeMarrais, J., Huang, M.-D.A.: Quantum computability. SIAM Journal on Computing 26(5), 1524–1540 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  3. Amano, M., Iwama, K.: Undecidability on quantum finite automata. In: STOC 1999: Proceedings of the thirty-first annual ACM symposium on Theory of computing, pp. 368–375. ACM, New York (1999)

    Chapter  Google Scholar 

  4. Ambainis, A., Beaudry, M., Golovkins, M., Ķikusts, A., Mercer, M., Thérien, D.: Algebraic results on quantum automata. Theory of Computing Systems 39(1), 165–188 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ambainis, A., Freivalds, R.: 1-way quantum finite automata: strengths, weaknesses and generalizations. In: FOCS 1998: Proceedings of the 39th Annual Symposium on Foundations of Computer Science, Palo Alto, California, pp. 332–341 (1998)

    Google Scholar 

  6. Ambainis, A., Watrous, J.: Two–way finite automata with quantum and classical states. Theoretical Computer Science 287(1), 299–311 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bernstein, E., Vazirani, U.: Quantum complexity theory. SIAM Journal on Computing 26(5) (1997)

    Google Scholar 

  8. Bertoni, A., Carpentieri, M.: Analogies and differences between quantum and stochastic automata. Theoretical Computer Science 262(1-2), 69–81 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bertoni, A., Mereghetti, C., Palano, B.: Quantum computing: 1-way quantum automata. In: Ésik, Z., Fülöp, Z. (eds.) DLT 2003. LNCS, vol. 2710, pp. 1–20. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  10. Brodsky, A., Pippenger, N.: Characterizations of 1–way quantum finite automata. SIAM Journal on Computing 31(5), 1456–1478 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. Freivalds, R., Karpinski, M.: Lower space bounds for randomized computation. In: Shamir, E., Abiteboul, S. (eds.) ICALP 1994. LNCS, vol. 820, pp. 580–592. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  12. Kaņeps, J.: Stochasticity of the languages acceptable by two-way finite probabilistic automata. Diskretnaya Matematika 1, 63–67 (1989) (in Russian)

    Google Scholar 

  13. Kondacs, A., Watrous, J.: On the power of quantum finite state automata. In: FOCS 1997: Proceedings of the 38th Annual Symposium on Foundations of Computer Science, Miami, Florida, pp. 66–75 (1997)

    Google Scholar 

  14. Kuklin, Y.I.: Two-way probabilistic automata. Avtomatika i vyc̆istitelnaja tekhnika 5, 36 (1973) (in Russian)

    Google Scholar 

  15. Li, L., Qiu, D.: Determining the equivalence for one-way quantum finite automata. Theoretical Computer Science 403(1), 42–51 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Meyer, A.R., Fischer, M.J.: Economy of description by automata, grammars, and formal systems. In: 12th Annual Symposium on Switching and Automata Theory, East Lansing, MI, USA, pp. 188–191 (1971)

    Google Scholar 

  17. Moore, C., Crutchfield, J.P.: Quantum automata and quantum grammars. Theoretical Computer Science 237(1-2), 275–306 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  18. Nasu, M., Honda, N.: A context-free language which is not acceptable by a probabilistic automaton. Information and Control 18(3), 233–236 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  19. Nayak, A.: Optimal lower bounds for quantum automata and random access codes. In: FOCS 1999: Proceedings of the 40th Annual Symposium on Foundations of Computer Science, Washington, DC, USA, pp. 369–376. IEEE Computer Society, Los Alamitos (1999)

    Google Scholar 

  20. Paschen, K.: Quantum finite automata using ancilla qubits. Technical report, University of Karlsruhe (2000)

    Google Scholar 

  21. Paz, A.: Introduction to Probabilistic Automata. Academic Press, New York (1971)

    MATH  Google Scholar 

  22. Rabin, M.O.: Probabilistic automata. Information and Control 6, 230–243 (1963)

    Article  MATH  Google Scholar 

  23. Turakainen, P.: Generalized automata and stochastic languages. Proceedings of the American Mathematical Society 21, 303–309 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  24. Watrous, J.: Space-bounded quantum complexity. Journal of Computer and System Sciences 59(2), 281–326 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  25. Yakaryılmaz, A., Cem Say, A.C.: Languages recognized with unbounded error by quantum finite automata. Technical report (2008) arXiv:0809.0073v2

    Google Scholar 

  26. Yakaryılmaz, A., Cem Say, A.C.: Language recognition by generalized quantum finite automata with unbounded error. In: 4th Workshop on Theory of Quantum Computation, Communication, and Cryptography, TQC 2009, Waterloo, Ontario, Canada (2009) (forthcoming)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Engineering, Bog̃aziçi University, Bebek, 34342, İstanbul, Turkey

    Abuzer Yakaryilmaz & A. C. Cem Say

Authors
  1. Abuzer Yakaryilmaz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. C. Cem Say
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, 4 Koptyug av, 630090, Novosibirsk, Russia

    Anna Frid

  2. Sobolev Institute of Mathematics SB RAS, Koptyug av. 4, 630090, Novosibirsk, Russia

    Andrey Morozov

  3. Max Planck Institute for Software Systems, Campus E1 4, 66123, Saarbrücken, Germany

    Andrey Rybalchenko

  4. Lehrstuhl für Theoretische Informatik, Institut für Informatik, Julius-Maximilians-Universität Würzburg, Am Hubland, 97974, Würzburg, Germany

    Klaus W. Wagner

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Yakaryilmaz, A., Say, A.C.C. (2009). Languages Recognized with Unbounded Error by Quantum Finite Automata. In: Frid, A., Morozov, A., Rybalchenko, A., Wagner, K.W. (eds) Computer Science - Theory and Applications. CSR 2009. Lecture Notes in Computer Science, vol 5675. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03351-3_33

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-03351-3_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03350-6

  • Online ISBN: 978-3-642-03351-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation