Skip to main content
SpringerLink
Log in
Book cover

International Computing and Combinatorics Conference

COCOON 2006: Computing and Combinatorics pp 83–93Cite as

Varieties Generated by Certain Models of Reversible Finite Automata

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4112))

Abstract

Reversible finite automata with halting states (RFA) were first considered by Ambainis and Freivalds to facilitate the research of Kondacs-Watrous quantum finite automata. In this paper we consider some of the algebraic properties of RFA, namely the varieties these automata generate. Consequently, we obtain a characterization of the boolean closure of the classes of languages recognized by these models.

This is a preview of subscription content, 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Almeida, J.: Finite Semigroups and Universal Algebra. World Scientific, Singapore (1994)

    MATH  Google Scholar 

  2. Almeida, J., Pin, J.E., Weil, P.: Semigroups whose Idempotents Form a Subsemigroup. Math. Proc. Camb. Phil. Soc. 111, 241–253 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  3. Ambainis, A., Beaudry, M., Golovkins, M., Ķikusts, A., Mercer, M., Thérien, D.: Algebraic Results on Quantum Automata. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 93–104. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  4. Ambainis, A., Bonner, R.F., Freivalds, R., Ķikusts, A.: Probabilities to Accept Languages by Quantum Finite Automata. In: Asano, T., Imai, H., Lee, D.T., Nakano, S.-i., Tokuyama, T. (eds.) COCOON 1999. LNCS, vol. 1627, pp. 174–183. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  5. Ambainis, A., Freivalds, R.: 1-Way Quantum Finite Automata: Strengths, Weaknesses and Generalizations. In: Proc. 39th FOCS, pp. 332–341 (1998)

    Google Scholar 

  6. Ambainis, A., Nayak, A., Ta-Shma, A., Vazirani, U.: Dense Quantum Coding and Quantum Finite Automata. Journal of the ACM 49(4), 496–511 (2002)

    Article  MathSciNet  Google Scholar 

  7. Ash, C.J.: Finite Semigroups with Commuting Idempotents. J. Austral. Math. Soc. (Series A) 43, 81–90 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bertoni, A., Mereghetti, C., Palano, B.: Quantum Computing: 1-Way Quantum Finite Automata. In: Ésik, Z., Fülöp, Z. (eds.) DLT 2003. LNCS, vol. 2710, pp. 1–20. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  9. Brodsky, A., Pippenger, N.: Characterizations of 1-Way Quantum Finite Automata. SIAM Journal on Computing 31(5), 1456–1478 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  10. Golovkins, M., Kravtsev, M.: Probabilistic Reversible Automata and Quantum Automata. In: Ibarra, O.H., Zhang, L. (eds.) COCOON 2002. LNCS, vol. 2387, pp. 574–583. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  11. Kondacs, A., Watrous, J.: On The Power of Quantum Finite State Automata. In: Proc. 38th FOCS, pp. 66–75 (1997)

    Google Scholar 

  12. Margolis, S.W., Pin, J.E.: Inverse Semigroups and Varieties of Finite Semigroups. Journal of Algebra 110, 306–323 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  13. Moore, C., Crutchfield, J.P.: Quantum Automata and Quantum Grammars. Theoretical Computer Science 237(1-2), 275–306 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  14. Nayak, A.: Optimal Lower Bounds for Quantum Automata and Random Access Codes. In: Proc. 40th FOCS, pp. 369–377 (1999)

    Google Scholar 

  15. Pin, J.E.: Varieties of Formal Langages. North Oxford, London and Plenum, New York (1986)

    Google Scholar 

  16. Pin, J.E.: On the Languages Accepted by Finite Reversible Automata. In: Ottmann, T. (ed.) ICALP 1987. LNCS, vol. 267, pp. 237–249. Springer, Heidelberg (1987)

    Google Scholar 

  17. Pin, J.E.: On Reversible Automata. In: Simon, I. (ed.) LATIN 1992. LNCS, vol. 583, pp. 401–416. Springer, Heidelberg (1992)

    Chapter  Google Scholar 

  18. Pin, J.E.: Eilenberg’s Theorem for Positive Varieties of Languages. Russian Mathematics (Iz. VUZ) 39(1), 80–90 (1995)

    MathSciNet  Google Scholar 

  19. Pin, J.E., Weil, P.: Semidirect Products of Ordered Semigroups. Communications in Algebra 30(1), 149–169 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  20. Pin, J.E., Weil, P.: The Wreath Product Principle for Ordered Semigroups. Communications in Algebra 30(12), 5677–5713 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  21. Polák, L.: Syntactic Semiring of a Language. In: Sgall, J., Pultr, A., Kolman, P. (eds.) MFCS 2001. LNCS, vol. 2136, pp. 611–620. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  22. Preston, G.B.: Inverse Semi-groups with Minimal Right Ideals. J. London Math. Soc. 29, 404–411 (1954)

    Article  MATH  MathSciNet  Google Scholar 

  23. Vagner, V.V.: Generalized Groups. Dokl. Akad. Nauk SSSR 84(6), 1119–1122 (1952)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Computer Science, University of Latvia, Raiņa bulv. 29, Riga, Latvia

    Marats Golovkins

  2. LIAFA, Université Paris VII and CNRS, Case 7014, 2 Place Jussieu, 75251 Cedex 05, Paris, France

    Jean-Eric Pin

Authors
  1. Marats Golovkins
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jean-Eric Pin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Notre Dame, IN 46556, Notre Dame, USA

    Danny Z. Chen

  2. Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan

    D. T. Lee

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Golovkins, M., Pin, JE. (2006). Varieties Generated by Certain Models of Reversible Finite Automata. In: Chen, D.Z., Lee, D.T. (eds) Computing and Combinatorics. COCOON 2006. Lecture Notes in Computer Science, vol 4112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11809678_11

Download citation

  • DOI: https://doi.org/10.1007/11809678_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-36925-7

  • Online ISBN: 978-3-540-36926-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation