A finite alternation result for reversible boolean circuits
Emerging Technologies
2018-06-27 v3 Quantum Physics
Abstract
We say that a reversible boolean function on n bits has alternation depth d if it can be written as the sequential composition of d reversible boolean functions, each of which acts only on the top n-1 bits or on the bottom n-1 bits. Moreover, if the functions on n-1 bits are even, we speak of even alternation depth. We show that every even reversible boolean function of n >= 4 bits has alternation depth at most 9 and even alternation depth at most 13.
Keywords
Cite
@article{arxiv.1604.02549,
title = {A finite alternation result for reversible boolean circuits},
author = {Peter Selinger},
journal= {arXiv preprint arXiv:1604.02549},
year = {2018}
}
Comments
19 pages. An earlier version of this paper appeared in Reversible Computation 2016. v2: added even alternation depth. v3: minor typos fixed