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Universality of 2-State 3-Symbol Reversible Logic Elements — A Direct Simulation Method of a Rotary Element

  • Tsuyoshi Ogiro
  • Artiom Alhazov
  • Tsuyoshi Tanizawa
  • Kenichi Morita
Conference paper
Part of the Proceedings in Information and Communications Technology book series (PICT, volume 2)

Abstract

A reversible logic element is a primitive from which reversible computing systems can be constructed. A rotary element is a typical 2-state 4-symbol reversible element with logical universality, and we can construct reversible Turing machines from it very simply. There are also many other reversible element with 1-bit memory. So far, it is known that all the 14 kinds of non-degenerate 2-state 3-symbol reversible elements can simulate a Fredkin gate, and hence they are universal. In this paper, we show that all these 14 elements can “directly” simulate a rotary element in a simple and systematic way.

Keywords

Reversible logic element reversible computing rotary element 

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References

  1. 1.
    Bennett, C.H.: Logical reversibility of computation. IBM J. Res. Dev. 17, 525–532 (1973)zbMATHCrossRefGoogle Scholar
  2. 2.
    Bennett, C.H.: Notes on the history of reversible computation. IBM J. Res. Dev. 32, 16–23 (1988)Google Scholar
  3. 3.
    Fredkin, E., Toffoli, T.: Conservative logic. Int. J. Theoret. Phys. 21, 219–253 (1982)CrossRefMathSciNetzbMATHGoogle Scholar
  4. 4.
    Lee, J., Peper, F., Adachi, S., Morita, K.: An asynchronous cellular automaton implementing 2-state 2-input 2-output reversed-twin reversible elements. In: Umeo, H., Morishita, S., Nishinari, K., Komatsuzaki, T., Bandini, S. (eds.) ACRI 2008. LNCS, vol. 5191, pp. 67–76. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  5. 5.
    Morita, K.: A simple construction method of a reversible finite automaton out of Fredkin gates, and its related problem. Trans. IEICE Japan E-73, 978–984 (1990)Google Scholar
  6. 6.
    Morita, K.: A simple reversible logic element and cellular automata for reversible computing. In: Margenstern, M., Rogozhin, Y. (eds.) MCU 2001. LNCS, vol. 2055, pp. 102–113. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  7. 7.
    Morita, K., Ogiro, T., Tanaka, K., Kato, H.: Classification and universality of reversible logic elements with one-bit memory. In: Margenstern, M. (ed.) MCU 2004. LNCS, vol. 3354, pp. 245–256. Springer, Heidelberg (2005)Google Scholar
  8. 8.
    Morita, K.: Reversible computing and cellular automata — a survey. Theoretical Computer Science 395, 101–131 (2008)CrossRefMathSciNetzbMATHGoogle Scholar
  9. 9.
    Ogiro, T., Kanno, A., Tanaka, K., Kato, H., Morita, K.: Nondegenerate 2-state 3-symbol reversible logic elements are all universal. Int. Journ. of Unconventional Computing 1, 47–67 (2005)Google Scholar
  10. 10.
    Petri, C.A.: Grundsätzliches zur Beschreibung diskreter Prozesse. In: Proc. 3rd Colloquium über Automatentheorie, pp. 121–140. Birkhäuser Verlag, Basel (1967)Google Scholar
  11. 11.
    Toffoli, T.: Reversible computing. In: de Bakker, J.W., van Leeuwen, J. (eds.) ICALP 1980. LNCS, vol. 85, pp. 632–644. Springer, Heidelberg (1980)Google Scholar
  12. 12.
    Toffoli, T.: Bicontinuous extensions of invertible combinatorial functions. Mathematical Systems Theory 14, 12–23 (1981)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Tokyo 2010

Authors and Affiliations

  • Tsuyoshi Ogiro
    • 1
  • Artiom Alhazov
    • 1
    • 2
  • Tsuyoshi Tanizawa
    • 1
  • Kenichi Morita
    • 1
  1. 1.Graduate School of Engineering, Higashi-HiroshimaHiroshima UniversityJapan
  2. 2.Institute of Mathematics and Computer ScienceAcademy of Sciences of MoldovaMoldova

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