On the Complexity of the Permanent in Various Computational Models

Ikenmeyer, Christian; Landsberg, J. M.

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On the Complexity of the Permanent in Various Computational Models

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

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arXiv:1610.00159.pdf
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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: https://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.