Advertisement

Fast One-Way Cellular Automata with Reversible Mealy Cells

  • Martin Kutrib
  • Andreas MalcherEmail author
  • Matthias Wendlandt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10248)

Abstract

We investigate cellular automata that are composed of reversible components with regard to the recognition of formal languages. In particular, real-time one-way cellular automata (\(\text {OCA}\)) are considered which are composed of reversible Mealy automata. Moreover, we differentiate between three notions of reversibility in the Mealy automata, namely, between weak and strong reversibility as well as reversible partitioned \(\text {OCA}\) which have been introduced by Morita in [14]. Here, it turns out that every real-time \(\text {OCA}\) can be transformed into an equivalent real-time \(\text {OCA}\) with weakly reversible automata in its cells, whereas the remaining two notions seem to be weaker. However, a non-semilinear language is provided that can be accepted by a real-time \(\text {OCA}\) with strongly reversible cells. On the other hand, we present a context-free, non-regular language that is accepted by some real-time reversible partitioned \(\text {OCA}\).

Notes

Acknowledgments

We greatly acknowledge the valuable comments of the anonymous reviewers which, in particular, helped to improve the result of Theorem 4.

References

  1. 1.
    Abramsky, S.: A structural approach to reversible computation. Theor. Comput. Sci. 347(3), 441–464 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Angluin, D.: Inference of reversible languages. J. ACM 29(3), 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.
    Kari, J.: Theory of cellular automata: a survey. Theor. Comput. Sci. 334(1–3), 3–33 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    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
  6. 6.
    Kutrib, M., Malcher, A.: Fast reversible language recognition using cellular automata. Inform. Comput. 206(9–10), 1142–1151 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Kutrib, M., Malcher, A.: Real-time reversible iterative arrays. Theor. Comput. Sci. 411, 812–822 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Kutrib, M., Malcher, A.: Reversible pushdown automata. J. Comput. System Sci. 78, 1814–1827 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Kutrib, M., Malcher, A.: One-way reversible multi-head finite automata. Theor. Comput. Sci. (to appear)Google Scholar
  10. 10.
    Kutrib, M., Malcher, A., Wendlandt, M.: Real-time reversible one-way cellular automata. In: Isokawa, T., Imai, K., Matsui, N., Peper, F., Umeo, H. (eds.) AUTOMATA 2014. LNCS, vol. 8996, pp. 56–69. Springer, Cham (2015). doi: 10.1007/978-3-319-18812-6_5 CrossRefGoogle Scholar
  11. 11.
    Kutrib, M., Malcher, A., Wendlandt, M.: Reversible queue automata. Fund. Inform. 148(3–4), 341–368 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Landauer, R.: Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5, 183–191 (1961)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Lange, K.J., McKenzie, P., Tapp, A.: Reversible space equals deterministic space. J. Comput. System Sci. 60, 354–367 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Morita, K.: Computation-universality of one-dimensional one-way reversible cellular automata. Inf. Process. Lett. 42, 325–329 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Morita, K.: Reversible simulation of one-dimensional irreversible cellular automata. Theor. Comput. Sci. 148(1), 157–163 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Morita, K.: Reversible computing and cellular automata - a survey. Theor. Comput. Sci. 395, 101–131 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Morita, K.: Two-way reversible multi-head finite automata. Fund. Inform. 110, 241–254 (2011)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Morita, K.: Language recognition by reversible partitioned cellular automata. In: Isokawa, T., Imai, K., Matsui, N., Peper, F., Umeo, H. (eds.) AUTOMATA 2014. LNCS, vol. 8996, pp. 106–120. Springer, Cham (2015). doi: 10.1007/978-3-319-18812-6_9 CrossRefGoogle Scholar
  19. 19.
    Morita, K., Harao, M.: Computation universality of one dimensional reversible injective cellular automata. IEICE Trans. Inf. Syst. E 72(1), 758–762 (1989)Google Scholar
  20. 20.
    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
  21. 21.
    Toffoli, T.: Computation and construction universality of reversible cellular automata. J. Comput. System Sci. 15, 213–231 (1977)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2017

Authors and Affiliations

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

Personalised recommendations