Skip to main content

Reversibility for stateless ordered RRWW-automata

Abstract

There are two types of stateless deterministic ordered restarting automata that both characterize the class of regular languages: the stl-det-ORWW-automaton and the stl-det-ORRWW-automaton. For the former a notion of reversibility has been introduced and studied that is very much tuned to the way in which restarting automata work. Here we suggest another, more classical, notion of reversibility for stl-det-ORRWW-automata, and we show that each regular language is accepted by such a reversible stl-det-ORRWW-automaton. We study the descriptional complexity of these automata, showing that they are exponentially more succinct than nondeterministic finite-state acceptors. We also look at the case of unary input alphabets.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    Bennett, C.: Logical reversibiliy of computation. IBM J. Res. Dev. 17, 525–532 (1973)

    Article  Google Scholar 

  2. 2.

    Chrobak, M.: Finite automata and unary languages. Theor. Comput. Sci. 47, 149–158 (1986)

    MathSciNet  Article  Google Scholar 

  3. 3.

    Ellul, K., Krawetz, B., Shallit, J., Wang, M.: Regular expressions: new results and open problems. J. Autom. Lang. Comb. 10, 407–437 (2005)

    MathSciNet  MATH  Google Scholar 

  4. 4.

    Jančar, P., Mráz, F., Plátek, M., Vogel, J.: Restarting automata. In: Reichel, H. (ed.) FCT’95, Proceedings. Lecture Notes in Computer Science, vol. 965, pp. 283–292. Springer, Heidelberg (1995)

  5. 5.

    Kutrib, M., Malcher, A.: Reversible pushdown automata. J. Comput. Syst. Sci. 78, 1814–1827 (2012)

    MathSciNet  Article  Google Scholar 

  6. 6.

    Kutrib, M., Malcher, A., Wendlandt, M.: Reversible queue automata. In: Bensch, S., Freund, R., Otto, F. (eds.) Sixth Workshop on Non-Classical Models of Automata and Applications \((\)NCMA 2014\()\) Proc., books@ocg.at, vol. 304, pp. 163–178. Österreichische Computer Gesellschaft, Wien (2014)

  7. 7.

    Kutrib, M., Messerschmidt, H., Otto, F.: On stateless deterministic restarting automata. Acta Inf. 47, 391–412 (2010)

    MathSciNet  Article  Google Scholar 

  8. 8.

    Kwee, K., Otto, F.: On some decision problems for stateless deterministic ordered restarting automata. In: Shallit, J., Okhotin, A. (eds.) DCFS 2015, Proceedings. Lecture Notes in Computer Science, vol. 9118, pp. 165–176. Springer, Heidelberg (2015)

  9. 9.

    Kwee, K., Otto, F.: On ordered RRWW-automata. In: Brlek, S., Reutenauer, C. (eds.) DLT 2016, Proceedings. Lecture Notes in Computer Science, vol. 9840, pp. 268–279. Springer, Heidelberg (2016)

  10. 10.

    Landau, E.: Über die Maximalordnung der Permutationen gegebenen Grades. Arch. Math. Phys. 3, 92–103 (1903)

    MATH  Google Scholar 

  11. 11.

    Landau, E.: Handbuch von der Lehre der Verteilung der Primzahlen, vol. I. Teubner, Leipzig (1909)

    MATH  Google Scholar 

  12. 12.

    Miller, W.: The maximum order of an element of a finite symmetric group. Am. Math. Mon. 94, 497–506 (1987)

    MathSciNet  Article  Google Scholar 

  13. 13.

    Mráz, F., Otto, F.: Ordered restarting automata for picture languages. In: Geffert, V., Preneel, B., Rovan, B., Štuller, J., Min Tjoa, A. (eds.) SOFSEM 2014, Proceedings. Lecture Notes in Computer Science, vol. 8327, pp. 431–442. Springer, Heidelberg (2014)

  14. 14.

    Otto, F.: Restarting automata. In: Ésik, Z., Martín-Vide, C., Mitrana, V. (eds.) Recent Advances in Formal Languages and Applications, Studies in Computational Intelligence, vol. 25, pp. 269–303. Springer, Heidelberg (2006)

    Google Scholar 

  15. 15.

    Otto, F.: On the descriptional complexity of deterministic ordered restarting automata. In: Jürgensen, H., Karhumäki, J., Okhotin, A. (eds.) DCFS 2014, Proceedings. Lecture Notes in Computer Science, vol. 8614, pp. 318–329. Springer, Heidelberg (2014)

  16. 16.

    Otto, F., Kwee, K.: On the descriptional complexity of stateless ordered restarting automata. Inf. Comput. 259, 277–302 (2018)

    MathSciNet  Article  Google Scholar 

  17. 17.

    Otto, F., Wendlandt, M., Kwee, K.: Reversible ordered restarting automata. In: Krivine, J., Stefani, J. (eds.) RC 2015, Proceedings. Lecture Notes in Computer Science, vol. 9138, pp. 60–75. Springer, Heidelberg (2015)

  18. 18.

    Pin, J.E.: On reversible automata. In: Simon, I. (ed.) LATIN’92, Proceedings. Lecture Notes in Computer Science, vol. 583, pp. 401–416. Springer, Heidelberg (1992)

  19. 19.

    Průša, D.: Weight-reducing Hennie machines and their descriptional complexity. In: Dediu, A.H., Martín-Vide, C., Sierra-Rodríguez, J., Truthe, B. (eds.) LATA 2014 Proceedings. Lecture Notes in Computer Science, vol. 8370, pp. 553–564. Springer, Heidelberg (2014)

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Friedrich Otto.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Otto, F., Wendlandt, M. Reversibility for stateless ordered RRWW-automata. Acta Informatica 58, 397–425 (2021). https://doi.org/10.1007/s00236-020-00389-0

Download citation

Mathematics Subject Classification

  • 68Q68
  • 68Q45
  • 68Q19