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.
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Ogiro, T., Alhazov, A., Tanizawa, T., Morita, K. (2010). Universality of 2-State 3-Symbol Reversible Logic Elements — A Direct Simulation Method of a Rotary Element. In: Peper, F., Umeo, H., Matsui, N., Isokawa, T. (eds) Natural Computing. Proceedings in Information and Communications Technology, vol 2. Springer, Tokyo. https://doi.org/10.1007/978-4-431-53868-4_29
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DOI: https://doi.org/10.1007/978-4-431-53868-4_29
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-53867-7
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