All reports by Author Andrew Morgan:

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TR22-158
| 18th November 2022
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Ivan Hu, Andrew Morgan, Dieter van Melkebeek#### Query Complexity of Inversion Minimization on Trees

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TR22-115
| 17th August 2022
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Dieter van Melkebeek, Andrew Morgan#### Polynomial Identity Testing via Evaluation of Rational Functions

Revisions: 2

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TR17-158
| 23rd October 2017
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Eric Allender, Joshua Grochow, Dieter van Melkebeek, Cris Moore, Andrew Morgan#### Minimum Circuit Size, Graph Isomorphism, and Related Problems

Ivan Hu, Andrew Morgan, Dieter van Melkebeek

We consider the following computational problem: Given a rooted tree and a ranking of its leaves, what is the minimum number of inversions of the leaves that can be attained by ordering the tree? This variation of the well-known problem of counting inversions in arrays originated in mathematical psychology. It ... more >>>

Dieter van Melkebeek, Andrew Morgan

We introduce a hitting set generator for Polynomial Identity Testing

based on evaluations of low-degree univariate rational functions at

abscissas associated with the variables. Despite the univariate

nature, we establish an equivalence up to rescaling with a generator

introduced by Shpilka and Volkovich, which has a similar structure but

uses ...
more >>>

Eric Allender, Joshua Grochow, Dieter van Melkebeek, Cris Moore, Andrew Morgan

We study the computational power of deciding whether a given truth-table can be described by a circuit of a given size (the Minimum Circuit Size Problem, or MCSP for short), and of the variant denoted as MKTP where circuit size is replaced by a polynomially-related Kolmogorov measure. All prior reductions ... more >>>