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)


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.


Reversible logic element reversible computing rotary element 


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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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