Fredkin Gates for Finite-valued Reversible and Conservative Logics
Quantum Physics
2009-11-07 v1
Abstract
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.
Cite
@article{arxiv.quant-ph/0205139,
title = {Fredkin Gates for Finite-valued Reversible and Conservative Logics},
author = {Gianpiero Cattaneo and Alberto Leporati and Roberto Leporini},
journal= {arXiv preprint arXiv:quant-ph/0205139},
year = {2009}
}
Comments
57 pages, 10 figures, 16 tables, 2 diagrams