All reports by Author Matthew Anderson:

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TR15-184
| 21st November 2015
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Matthew Anderson, Michael Forbes, Ramprasad Saptharishi, Amir Shpilka, Ben Lee Volk#### Identity Testing and Lower Bounds for Read-$k$ Oblivious Algebraic Branching Programs

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TR11-158
| 25th November 2011
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Matthew Anderson, Dieter van Melkebeek, Nicole Schweikardt, Luc Segoufin#### Locality from Circuit Lower Bounds

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TR10-188
| 8th December 2010
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Matthew Anderson, Dieter van Melkebeek, Ilya Volkovich#### Derandomizing Polynomial Identity Testing for Multilinear Constant-Read Formulae

Revisions: 1

Matthew Anderson, Michael Forbes, Ramprasad Saptharishi, Amir Shpilka, Ben Lee Volk

Read-$k$ oblivious algebraic branching programs are a natural generalization of the well-studied model of read-once oblivious algebraic branching program (ROABPs).

In this work, we give an exponential lower bound of $\exp(n/k^{O(k)})$ on the width of any read-$k$ oblivious ABP computing some explicit multilinear polynomial $f$ that is computed by a ...
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Matthew Anderson, Dieter van Melkebeek, Nicole Schweikardt, Luc Segoufin

We study the locality of an extension of first-order logic that captures graph queries computable in AC$^0$, i.e., by families of polynomial-size constant-depth circuits. The extension considers first-order formulas over relational structures which may use arbitrary numerical predicates in such a way that their truth value is independent of the ... more >>>

Matthew Anderson, Dieter van Melkebeek, Ilya Volkovich

We present a polynomial-time deterministic algorithm for testing whether constant-read multilinear arithmetic formulae are identically zero. In such a formula each variable occurs only a constant number of times and each subformula computes a multilinear polynomial. Our algorithm runs in time $s^{O(1)}\cdot n^{k^{O(k)}}$, where $s$ denotes the size of the ... more >>>