Complexity of linear circuits and geometry

10 Mar 2015  ·  Gesmundo Fulvio, Hauenstein Jonathan, Ikenmeyer Christian, Landsberg JM ·

We use algebraic geometry to study matrix rigidity, and more generally, the complexity of computing a matrix-vector product, continuing a study initiated by Kumar, et. al. We (i) exhibit many non-obvious equations testing for (border) rigidity, (ii) compute degrees of varieties associated to rigidity, (iii) describe algebraic varieties associated to families of matrices that are expected to have super-linear rigidity, and (iv) prove results about the ideals and degrees of cones that are of interest in their own right...

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Computational Complexity Algebraic Geometry

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