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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

R2 v1 2026-06-22T13:28:32.900Z