Fredkin Gates for Finite-valued Reversible and Conservative Logics

Details Fredkin Gates for Finite-valued Reversible and Conservative Logics Fredkin Gates for Finite-valued Reversible and Conservative Logics

2002-05-22

arxiv.org/abs/quant-ph/0205139v1

Physics

Quantum Physics

57 pages, 10 figures, 16 tables, 2 diagrams

Scientific paper

10.1088/0305-4470/35/46/304

The basic principles and results of Conservative Logic introduced by Fredkin and Toffoli on the basis of a seminal paper of Landauer are extended to d-valued logics, with a special attention to three-valued logics. Different approaches to d-valued logics are examined in order to determine some possible universal sets of logic primitives. In particular, we consider the typical connectives of Lukasiewicz and Godel logics, as well as Chang's MV-algebras. As a result, some possible three-valued and d-valued universal gates are described which realize a functionally complete set of fundamental connectives.

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