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On the Complexity of the Permanent in Various Computational Models

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons202366

Ikenmeyer,  Christian
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Fulltext (public)

arXiv:1610.00159.pdf
(Preprint), 217KB

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Citation

Ikenmeyer, C., & Landsberg, J. M. (2016). On the Complexity of the Permanent in Various Computational Models. Retrieved from http://arxiv.org/abs/1610.00159.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002C-4F1E-C
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.