Transducing Reversibly with Finite State Machines

  • Martin Kutrib
  • Andreas Malcher
  • Matthias Wendlandt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10329)

Abstract

Finite state machines are investigated towards their ability to reversibly compute transductions, that is, to transform inputs into outputs in a reversible way. This means that the transducers are backward deterministic and hence are able to uniquely step the computation back and forth. The families of transductions computed are classified with regard to three types of length-preserving transductions as well as to the property of working reversibly. It is possible to settle all inclusion relations between the families of transductions. Finally, the standard closure properties are investigated and the non-closure under almost all operations can be shown.

References

  1. 1.
    Aho, A.V., Hopcroft, J.E., Ullman, J.D.: A general theory of translation. Math. Syst. Theor. 3, 193–221 (1969)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Aho, A.V., Ullman, J.D.: The theory of parsing, translation, and compiling. Parsing, vol. I. Prentice-Hall (1972)Google Scholar
  3. 3.
    Angluin, D.: Inference of reversible languages. J. ACM 29, 741–765 (1982)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Axelsen, H.B., Jakobi, S., Kutrib, M., Malcher, A.: A hierarchy of fast reversible turing machines. In: Krivine, J., Stefani, J.-B. (eds.) RC 2015. LNCS, vol. 9138, pp. 29–44. Springer, Cham (2015). doi:10.1007/978-3-319-20860-2_2 CrossRefGoogle Scholar
  5. 5.
    Bennett, C.H.: Logical reversibility of computation. IBM J. Res. Dev. 17, 525–532 (1973)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Bensch, S., Björklund, J., Kutrib, M.: Deterministic stack transducers. In: Han, Y.-S., Salomaa, K. (eds.) CIAA 2016. LNCS, vol. 9705, pp. 27–38. Springer, Cham (2016). doi:10.1007/978-3-319-40946-7_3 CrossRefGoogle Scholar
  7. 7.
    Berstel, J.: Transductions and Context-Free-Languages. Teubner (1979)Google Scholar
  8. 8.
    Holzer, M., Jakobi, S., Kutrib, M.: Minimal reversible deterministic finite automata. In: Potapov, I. (ed.) DLT 2015. LNCS, vol. 9168, pp. 276–287. Springer, Cham (2015). doi:10.1007/978-3-319-21500-6_22 CrossRefGoogle Scholar
  9. 9.
    Kondacs, A., Watrous, J.: On the power of quantum finite state automata. In: Foundations of Computer Science (FOCS 1997), pp. 66–75. IEEE Computer Society (1997)Google Scholar
  10. 10.
    Kutrib, M., Malcher, A.: Reversible pushdown automata. J. Comput. System Sci. 78, 1814–1827 (2012)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Kutrib, M., Malcher, A.: One-dimensional cellular automaton transducers. Fundam. Inform. 126, 201–224 (2013)MathSciNetMATHGoogle Scholar
  12. 12.
    Kutrib, M., Malcher, A.: One-way reversible multi-head finite automata. Theor. Comput. Sci., to appearGoogle Scholar
  13. 13.
    Landauer, R.: Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5, 183–191 (1961)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Lange, K.J., McKenzie, P., Tapp, A.: Reversible space equals deterministic space. J. Comput. Syst. Sci. 60, 354–367 (2000)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Lecerf, Y.: Logique mathématique: machines de Turing réversible. C.R. Séances Acad. Sci. 257, 2597–2600 (1963)MathSciNetGoogle Scholar
  16. 16.
    Morita, K.: Two-way reversible multi-head finite automata. Fund. Inform. 110, 241–254 (2011)MathSciNetMATHGoogle Scholar
  17. 17.
    Pin, J.-E.: On reversible automata. In: Simon, I. (ed.) LATIN 1992. LNCS, vol. 583, pp. 401–416. Springer, Heidelberg (1992). doi:10.1007/BFb0023844 Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Martin Kutrib
    • 1
  • Andreas Malcher
    • 1
  • Matthias Wendlandt
    • 1
  1. 1.Institut für InformatikUniversität GiessenGiessenGermany

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