Boosting Reversible Pushdown Machines by Preprocessing

  • Holger Bock Axelsen
  • Martin Kutrib
  • Andreas MalcherEmail author
  • Matthias Wendlandt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9720)


It is well known that reversible finite automata do not accept all regular languages and that reversible pushdown automata do not accept all deterministic context-free languages. It is of significant interest both from a practical and theoretical point of view to close these gaps. We here extend these reversible models by a preprocessing unit which is basically a reversible injective and length-preserving sequential transducer. It turns out that preprocessing the input using such weak devices increases the computational power of reversible deterministic finite automata to the acceptance of all regular languages, whereas for reversible pushdown automata the accepted family of languages lies strictly in between the reversible deterministic context-free languages and the real-time deterministic context-free languages. Moreover, it is shown that the computational power of both types of machines is not changed by allowing the preprocessing sequential transducer to work irreversibly. Finally, we examine the closure properties of the family of languages accepted by such machines.



The authors acknowledge partial support from COST Action IC1405 Reversible Computation. H.B. Axelsen was supported by the Danish Council for Independent Research \(\mid \) Natural Sciences under the Foundations of Reversible Computing project, and by an IC1405 STSM (short-term scientific mission) grant.


  1. 1.
    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, Switzerland (2015)CrossRefGoogle Scholar
  2. 2.
    Ginsburg, S., Spanier, E.H.: Finite-turn pushdown automata. SIAM J. Control 4, 423–434 (1966)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Harrison, M.A.: Introduction to Formal Language Theory. Addison-Wesley, Reading (1978)zbMATHGoogle Scholar
  4. 4.
    Kondacs, A., Watrous, J.: On the power of quantum finite state automata. In: Proceeding of Foundations of Computer Science, pp. 66–75. IEEE (1997)Google Scholar
  5. 5.
    Kutrib, M.: Aspects of reversibility for classical automata. In: Calude, C.S., Freivalds, R., Kazuo, I. (eds.) Computing with New Resources. LNCS, vol. 8808, pp. 83–98. Springer, Heidelberg (2014)Google Scholar
  6. 6.
    Kutrib, M., Malcher, A.: Reversible pushdown automata. J. Comput. Syst. Sci. 78, 1814–1827 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Pin, J.E.: On reversible automata. In: Simon, I. (ed.) Latin 1992. LNCS, vol. 583, pp. 401–416. Springer, Heidelberg (1992)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Holger Bock Axelsen
    • 1
  • Martin Kutrib
    • 2
  • Andreas Malcher
    • 2
    Email author
  • Matthias Wendlandt
    • 2
  1. 1.Department of Computer ScienceUniversity of CopenhagenCopenhagen EDenmark
  2. 2.Institut für InformatikUniversität GiessenGiessenGermany

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