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REPORTS > AUTHORS > MICHAEL FORBES:
All reports by Author Michael Forbes:

TR14-162 | 28th November 2014
Michael Forbes, Venkatesan Guruswami

Dimension Expanders via Rank Condensers

An emerging theory of "linear-algebraic pseudorandomness" aims to understand the linear-algebraic analogs of fundamental Boolean pseudorandom objects where the rank of subspaces plays the role of the size of subsets. In this work, we study and highlight the interrelationships between several such algebraic objects such as subspace designs, dimension ... more >>>


TR13-132 | 23rd September 2013
Michael Forbes, Ramprasad Saptharishi, Amir Shpilka

Pseudorandomness for Multilinear Read-Once Algebraic Branching Programs, in any Order

We give deterministic black-box polynomial identity testing algorithms for multilinear read-once oblivious algebraic branching programs (ROABPs), in n^(lg^2 n) time. Further, our algorithm is oblivious to the order of the variables. This is the first sub-exponential time algorithm for this model. Furthermore, our result has no known analogue in the ... more >>>


TR13-033 | 1st March 2013
Michael Forbes, Amir Shpilka

Explicit Noether Normalization for Simultaneous Conjugation via Polynomial Identity Testing

Revisions: 1

Mulmuley recently gave an explicit version of Noether's Normalization lemma for ring of invariants of matrices under simultaneous conjugation, under the conjecture that there are deterministic black-box algorithms for polynomial identity testing (PIT). He argued that this gives evidence that constructing such algorithms for PIT is beyond current techniques. In ... more >>>


TR12-115 | 11th September 2012
Michael Forbes, Amir Shpilka

Quasipolynomial-time Identity Testing of Non-Commutative and Read-Once Oblivious Algebraic Branching Programs

Revisions: 1

We study the problem of obtaining efficient, deterministic, black-box polynomial identity testing (PIT) algorithms for read-once oblivious algebraic branching programs (ABPs). This class has an efficient, deterministic, white-box polynomial identity testing algorithm (due to Raz and Shpilka), but prior to this work had no known such black-box algorithm. Here we ... more >>>


TR11-147 | 2nd November 2011
Michael Forbes, Amir Shpilka

On Identity Testing of Tensors, Low-rank Recovery and Compressed Sensing

We study the problem of obtaining efficient, deterministic, black-box polynomial identity testing algorithms for depth-3 set-multilinear circuits (over arbitrary fields). This class of circuits has an efficient, deterministic, white-box polynomial identity testing algorithm (due to Raz and Shpilka), but has no known such black-box algorithm. We recast this problem as ... more >>>


TR11-110 | 10th August 2011
Alessandro Chiesa, Michael Forbes

Improved Soundness for QMA with Multiple Provers

Revisions: 1

We present three contributions to the understanding of QMA with multiple provers:

1) We give a tight soundness analysis of the protocol of [Blier and Tapp, ICQNM '09], yielding a soundness gap $\Omega(N^{-2})$, which is the best-known soundness gap for two-prover QMA protocols with logarithmic proof size. Maybe ... more >>>


TR11-010 | 1st February 2011
Boris Alexeev, Michael Forbes, Jacob Tsimerman

Tensor Rank: Some Lower and Upper Bounds

The results of Strassen and Raz show that good enough tensor rank lower bounds have implications for algebraic circuit/formula lower bounds.

We explore tensor rank lower and upper bounds, focusing on explicit tensors. For odd d, we construct field-independent explicit 0/1 tensors T:[n]^d->F with rank at least 2n^(floor(d/2))+n-Theta(d log n). ... more >>>




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