Real-Time Reversible One-Way Cellular Automata

  • Martin Kutrib
  • Andreas MalcherEmail author
  • Matthias Wendlandt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8996)


Real-time one-way cellular automata (\({\text {OCA}}\)) are investigated towards their ability to perform reversible computations with regard to formal language recognition. It turns out that the standard model with fixed boundary conditions is quite weak in terms of reversible information processing, since it is shown that in this case exactly the regular languages can be accepted reversibly. We then study a modest extension which allows that information may flow circularly from the leftmost cell into the rightmost cell. It is shown that this extension does not increase the computational power in the general case, but does increase it for reversible computations. On the other hand, the model is less powerful than real-time reversible two-way cellular automata. Additionally, we obtain that the corresponding language class is closed under Boolean operations, and we prove the undecidability of several decidability questions. Finally, it is shown that the reversibility of an arbitrary real-time circular one-way cellular automaton is undecidable as well.


Reversibility One-way cellular automata Language recognition Closure properties Decidability 


  1. 1.
    Amoroso, S., Patt, Y.N.: Decision procedures for surjectivity and injectivity of parallel maps for tesselation structures. J. Comput. System Sci. 6, 448–464 (1972)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Angluin, D.: Inference of reversible languages. J. ACM 29, 741–765 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bennett, C.H.: Logical reversibility of computation. IBM J. Res. Dev. 17, 525–532 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Choffrut, C., Čulik II, K.: On real-time cellular automata and trellis automata. Acta Inform. 21, 393–407 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Czeizler, E., Kari, J.: A tight linear bound on the neighborhood of inverse cellular automata. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 410–420. Springer, Heidelberg (2005) CrossRefGoogle Scholar
  6. 6.
    Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Cambridge (1979) zbMATHGoogle Scholar
  7. 7.
    Kari, J.: Reversibility and surjectivity problems of cellular automata. J. Comput. System Sci. 48, 149–182 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Kari, J.: Theory of cellular automata: a survey. Theoret. Comput. Sci. 334, 3–33 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Kutrib, M.: Cellular automata - a computational point of view. In: Bel-Enguix, G., Jiménez-López, M.D., Martín-Vide, C. (eds.) New Developments in Formal Languages and Applications. Studies in Computational Intelligence, vol. 113, pp. 183–227. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  10. 10.
    Kutrib, M.: Cellular automata and language theory. In: Meyers, R.A. (ed.) Encyclopedia of Complexity and System Science, pp. 800–823. Springer, New York (2009) CrossRefGoogle Scholar
  11. 11.
    Kutrib, M., Malcher, A.: Fast reversible language recognition using cellular automata. Inform. Comput. 206, 1142–1151 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Kutrib, M., Malcher, A.: Real-time reversible iterative arrays. Theoret. Comput. Sci. 411, 812–822 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Kutrib, M., Malcher, A.: Reversible pushdown automata. J. Comput. System Sci. 78, 1814–1827 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Kutrib, M., Malcher, A.: One-way reversible multi-head finite automata. In: Glück, R., Yokoyama, T. (eds.) RC 2012. LNCS, vol. 7581, pp. 14–28. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  15. 15.
    Landauer, R.: Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5, 183–191 (1961)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Lange, K.J., McKenzie, P., Tapp, A.: Reversible space equals deterministic space. J. Comput. System Sci. 60, 354–367 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Morita, K.: Reversible computing and cellular automata - a survey. Theoret. Comput. Sci. 395, 101–131 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Morita, K.: Two-way reversible multi-head finite automata. Fund. Inform. 110, 241–254 (2011)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Pin, J.-C.: On reversible automata. In: Simon, I. (ed.) LATIN 1992. LNCS, vol. 583, pp. 401–416. Springer, Heidelberg (1992) Google Scholar
  20. 20.
    Umeo, H., Morita, K., Sugata, K.: Deterministic one-way simulation of two-way real-time cellular automata and its related problems. Inform. Process. Lett. 14, 158–161 (1982)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Martin Kutrib
    • 1
  • Andreas Malcher
    • 1
    Email author
  • Matthias Wendlandt
    • 1
  1. 1.Institut Für InformatikUniversität GiessenGiessenGermany

Personalised recommendations