\input zb-basic
\input zb-ioport
\iteman{io-port 06028108}
\itemau{Morita, Kenichi; Ogiro, Tsuyoshi; Alhazov, Artiom; Tanizawa, Tsuyoshi}
\itemti{Non-degenerate 2-state reversible logic elements with three or more symbols are all universal.}
\itemso{J. Mult.-Val. Log. Soft Comput. 18, No. 1, 37-54 (2012).}
\itemab
Summary: A reversible logic element is a primitive from which reversible computing systems can be constructed. A rotary element is a typical one with 1-bit memory (hence it has 2 states) and with 4 input/output symbols. It is known that we can construct any reversible Turing machine by using only rotary elements very simply. In this sense it is a universal reversible logic element. There are also many other reversible elements with 1-bit memory. So far, it has been shown that all the 14 kinds of non-degenerate 2-state 3-symbol reversible elements can simulate a rotary element, and hence they are universal. In this paper, we generalize this result by showing that every non-degenerate 2-state $k$-symbol reversible logic element can simulate a rotary element if $k > 2$.
\itemrv{~}
\itemcc{}
\itemut{reversible logic element; universality; reversible computing; rotary element; reversible Turing machine}
\itemli{http://www.oldcitypublishing.com/MVLSC/MVLSCcontents/MVLSCv18n1contents.html}
\end