A Deterministic Two-Way Multi-head Finite Automaton Can Be Converted into a Reversible One with the Same Number of Heads

  • Kenichi Morita
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7581)


A two-way multi-head finite automaton (MFA) is a variant of a finite automaton consisting of a finite-state control, a finite number of heads that can move in two directions, and a read-only input tape. Here, we show that for any given deterministic MFA we can construct a reversible MFA with the same number of heads that accepts the same language as the former. We then apply this conversion method to a Turing machine. By this, we can obtain, in a simple way, an equivalent reversible Turing machine that is garbage-less, uses the same number of tape symbols, and uses the same amount of the storage tape.


multi-head finite automaton reversible computing reversible Turing machine garbage-less computation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Axelsen, H.: 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
  2. 2.
    Bennett, C.H.: Logical reversibility of computation. IBM J. Res. Dev. 17, 525–532 (1973)CrossRefzbMATHGoogle Scholar
  3. 3.
    Blum, M., Hewitt, C.: Automata on a two-dimensional tape. In: Proc. IEEE Symp. on Switching and Automata Theory, pp. 155–160. IEEE (1967)Google Scholar
  4. 4.
    Holzer, M., Kutrib, M., Malcher, A.: Complexity of multi-head finite automata: Origins and directions. Theoret. Comput. Sci. 412, 83–96 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Kondacs, A., Watrous, J.: On the power of quantum finite state automata. In: Proc. 36th FOCS, pp. 66–75. IEEE (1997)Google Scholar
  6. 6.
    Lange, K.J., McKenzie, P., Tapp, A.: Reversible space equals deterministic space. J. Comput. Syst. Sci. 60, 354–367 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Morita, K.: Two-way reversible multi-head finite automata. Fundamenta Informaticae 110, 241–254 (2011)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Sipser, M.: Halting space-bounded computations. Theoret. Comput. Sci. 10, 335–338 (1980)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Kenichi Morita
    • 1
  1. 1.Department of Information EngineeringHiroshima UniversityHigashi-HiroshimaJapan

Personalised recommendations