On the complexity of the permanent in various computational models

Christian Ikenmeyer; J. M. Landsberg

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arXiv · 1610.00159

On the complexity of the permanent in various computational models

Christian Ikenmeyer·J. M. Landsberg

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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.

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Christian Ikenmeyer, J. M. Landsberg. 2016-10-01. On the complexity of the permanent in various computational models. https://arxiv.org/abs/1610.00159

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