English

On the complexity of the permanent in various computational models

Computational Complexity 2016-10-04 v1

Abstract

We answer a question in [Landsberg, Ressayre, 2015], showing the regular determinantal complexity of the determinant det_m is O(m^3). We answer questions in, and generalize results of [Aravind, Joglekar, 2015], showing there is no rank one determinantal expression for perm_m or det_m when m >= 3. Finally we state and prove several "folklore" results relating different models of computation.

Cite

@article{arxiv.1610.00159,
  title  = {On the complexity of the permanent in various computational models},
  author = {Christian Ikenmeyer and J. M. Landsberg},
  journal= {arXiv preprint arXiv:1610.00159},
  year   = {2016}
}

Comments

18 pages

R2 v1 2026-06-22T16:07:38.786Z