Reversible and Irreversible Computations of Deterministic Finite-State Devices

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9234)

Abstract

Finite-state devices with a read-only input tape that may be equipped with further resources as queues or pushdown stores are considered towards their ability to perform reversible computations. Some aspects of the notion of logical reversibility are addressed. We present some selected results on the decidability, uniqueness, and size of minimal reversible deterministic finite automata. The relations and properties of reversible automata that are equipped with storages are discussed, where we exemplarily stick with the storage types queue and pushdown store. In particular, the computational capacities, decidability problems, and closure properties are the main topics covered, and we draw attention to the overall picture and some of the main ideas involved.

Keywords

Reversibility Finite state devices Minimality Queue and pushdown storage Decidability Closure properties 

References

  1. 1.
    Amoroso, S., Patt, Y.N.: Decision procedures for surjectivity and injectivity of parallel maps for tesselation structures. J. Comput. Syst. Sci. 6, 448–464 (1972)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Angluin, D.: Inference of reversible languages. J. ACM 29, 741–765 (1982)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Axelsen, H.B.: Reversible multi-head finite automata characterize reversible logarithmic space. In: Dediu, A.-H., Martín-Vide, C. (eds.) LATA 2012. LNCS, vol. 7183, pp. 95–105. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  4. 4.
    Axelsen, H.B., Glück, R.: A simple and efficient universal reversible turing machine. In: Dediu, A.-H., Inenaga, S., Martín-Vide, C. (eds.) LATA 2011. LNCS, vol. 6638, pp. 117–128. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  5. 5.
    Axelsen, H.B., Jakobi, S., Kutrib, M., Malcher, A.: A hierarchy of fast reversible turing machines. In: Krivine, J., Stefani, J.B. (eds.) Reversible Computation (RC 2015). LNCS, vol. 9138, pp. 29–44. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  6. 6.
    Bennett, C.H.: Logical reversibility of computation. IBM J. Res. Dev. 17, 525–532 (1973)CrossRefMATHGoogle Scholar
  7. 7.
    Bennett, C.H.: Time/space trade-offs for reversible computation. SIAM J. Comput. 18, 766–776 (1989)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Brandenburg, F.J.: Intersections of some families of languages. In: Kott, L. (ed.) International Colloquium on Automata, Languages and Programming (ICALP 1986). LNCS, vol. 226, pp. 60–68. Springer, Heidelberg (1986)CrossRefGoogle Scholar
  9. 9.
    Buhrman, H., Tromp, J., Vitányi, P.M.B.: Time and space bounds for reversible simulation. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 1017–1027. Springer, Heidelberg (2001) CrossRefGoogle Scholar
  10. 10.
    Cherubini, A., Citrini, C., Crespi-Reghizzi, S., Mandrioli, D.: QRT FIFO automata, breadth-first grammars and their relations. Theoret. Comput. Sci. 85, 171–203 (1991)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    García, P., de Parga, M.V., López, D.: On the efficient construction of quasi-reversible automata for reversible languages. Inform. Process. Lett. 107, 13–17 (2008)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Harrison, M.A.: Introduction to Formal Language Theory. Addison-Wesley, Reading (1978) MATHGoogle Scholar
  13. 13.
    Héam, P.C.: A lower bound for reversible automata. RAIRO Inform. Théor. 34, 331–341 (2000)CrossRefMATHGoogle Scholar
  14. 14.
    Holzer, M., Jakobi, S., Kutrib, M.: Minimal reversible deterministic finite automata. In: Potapov, I. (ed.) Developments in Language Theory (DLT 2015). LNCS, Springer (to appear 2015)Google Scholar
  15. 15.
    Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Boston (1979) MATHGoogle Scholar
  16. 16.
    Kari, J.: Reversibility and surjectivity problems of cellular automata. J. Comput. Syst. Sci. 48, 149–182 (1994)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Kari, J.: Reversible cellular automata. In: De Felice, C., Restivo, A. (eds.) DLT 2005. LNCS, vol. 3572, pp. 57–68. Springer, Heidelberg (2005) CrossRefGoogle Scholar
  18. 18.
    Kobayashi, S., Yokomori, T.: Learning approximately regular languages with reversible languages. Theoret. Comput. Sci. 174, 251–257 (1997)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    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
  20. 20.
    Kutrib, M.: Aspects of reversibility for classical automata. In: Calude, C.S., Freivalds, R., Kazuo, I. (eds.) Gruska Festschrift. LNCS, vol. 8808, pp. 83–98. Springer, Heidelberg (2014) Google Scholar
  21. 21.
    Kutrib, M., Malcher, A.: Fast reversible language recognition using cellular automata. Inform. Comput. 206, 1142–1151 (2008)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Kutrib, M., Malcher, A.: Real-time reversible iterative arrays. Theoret. Comput. Sci. 411, 812–822 (2010)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Kutrib, M., Malcher, A.: Reversible pushdown automata. J. Comput. Syst. Sci. 78, 1814–1827 (2012)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    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
  25. 25.
    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, Heidelberg (2015) CrossRefGoogle Scholar
  26. 26.
    Kutrib, M., Malcher, A., Wendlandt, M.: Reversible queue automata. In: Bensch, S., Freund, R., Otto, F. (eds.) Non-Classical Models of Automata and Applications (NCMA 2014), vol. 304, pp. 163–178. Austrian Computer Society, Vienna (2014). www.books@ocg.atGoogle Scholar
  27. 27.
    Kutrib, M., Wendlandt, M.: Reversible limited automata. In: Machines, Computations, and Universality (MCU 2015). LNCS, Springer (to appear, 2015)Google Scholar
  28. 28.
    Kutrib, M., Worsch, T.: Degrees of reversibility for DFA and DPDA. In: Yamashita, S., Minato, S. (eds.) RC 2014. LNCS, vol. 8507, pp. 40–53. Springer, Heidelberg (2014) Google Scholar
  29. 29.
    Landauer, R.: Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5, 183–191 (1961)MathSciNetCrossRefMATHGoogle Scholar
  30. 30.
    Lange, K.J., McKenzie, P., Tapp, A.: Reversible space equals deterministic space. J. Comput. Syst. Sci. 60, 354–367 (2000)MathSciNetCrossRefMATHGoogle Scholar
  31. 31.
    Li, M., Longpré, L., Vitányi, P.M.B.: The power of the queue. SIAM J. Comput. 21, 697–712 (1992)MathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    Lombardy, S.: On the construction of reversible automata for reversible languages. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, p. 170. Springer, Heidelberg (2002) CrossRefGoogle Scholar
  33. 33.
    Morita, K.: Reversible simulation of one-dimensional irreversible cellular automata. Theoret. Comput. Sci. 148, 157–163 (1995)MathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    Morita, K.: Reversible computing and cellular automata - a survey. Theoret. Comput. Sci. 395, 101–131 (2008)MathSciNetCrossRefMATHGoogle Scholar
  35. 35.
    Morita, K.: Two-way reversible multi-head finite automata. Fund. Inform. 110, 241–254 (2011)MathSciNetMATHGoogle Scholar
  36. 36.
    Pin, J.E.: On reversible automata. In: Simon, I. (ed.) LATIN 1992. LNCS, vol. 583, pp. 401–416. Springer, Heidelberg (1992) Google Scholar
  37. 37.
    Vollmar, R.: Über einen Automaten mit Pufferspeicherung. Computing 5, 57–70 (1970)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institut für InformatikUniversität GiessenGiessenGermany

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