All reports by Author Joshua Grochow:

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TR17-009
| 19th January 2017
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Joshua Grochow, Mrinal Kumar, Michael Saks, Shubhangi Saraf#### Towards an algebraic natural proofs barrier via polynomial identity testing

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TR16-162
| 18th October 2016
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Joshua Grochow#### NP-hard sets are not sparse unless P=NP: An exposition of a simple proof of Mahaney's Theorem, with applications

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TR15-171
| 28th October 2015
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Joshua Grochow#### Monotone projection lower bounds from extended formulation lower bounds

Revisions: 2
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Comments: 1

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TR15-162
| 9th October 2015
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Eric Allender, Joshua Grochow, Cris Moore#### Graph Isomorphism and Circuit Size

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TR14-052
| 14th April 2014
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Joshua Grochow, Toniann Pitassi#### Circuit complexity, proof complexity, and polynomial identity testing

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TR13-123
| 6th September 2013
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Joshua Grochow, Youming Qiao#### Algorithms for group isomorphism via group extensions and cohomology

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TR11-168
| 9th December 2011
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Joshua Grochow#### Lie algebra conjugacy

Joshua Grochow, Mrinal Kumar, Michael Saks, Shubhangi Saraf

We observe that a certain kind of algebraic proof - which covers essentially all known algebraic circuit lower bounds to date - cannot be used to prove lower bounds against VP if and only if what we call succinct hitting sets exist for VP. This is analogous to the Razborov-Rudich ... more >>>

Joshua Grochow

Mahaney's Theorem states that, assuming P $\neq$ NP, no NP-hard set can have a polynomially bounded number of yes-instances at each input length. We give an exposition of a very simple unpublished proof of Manindra Agrawal whose ideas appear in Agrawal-Arvind ("Geometric sets of low information content," Theoret. Comp. Sci., ... more >>>

Joshua Grochow

In this short note, we show that the permanent is not complete for non-negative polynomials in $VNP_{\mathbb{R}}$ under monotone p-projections. In particular, we show that Hamilton Cycle polynomial and the cut polynomials are not monotone p-projections of the permanent. To prove this we introduce a new connection between monotone projections ... more >>>

Eric Allender, Joshua Grochow, Cris Moore

We show that the Graph Automorphism problem is ZPP-reducible to MKTP, the problem of minimizing time-bounded Kolmogorov complexity. MKTP has previously been studied in connection with the Minimum Circuit Size Problem (MCSP) and is often viewed as essentially a different encoding of MCSP. All prior reductions to MCSP have applied ... more >>>

Joshua Grochow, Toniann Pitassi

We introduce a new and very natural algebraic proof system, which has tight connections to (algebraic) circuit complexity. In particular, we show that any super-polynomial lower bound on any Boolean tautology in our proof system implies that the permanent does not have polynomial-size algebraic circuits ($VNP \neq VP$). As a ... more >>>

Joshua Grochow, Youming Qiao

The isomorphism problem for groups given by multiplication tables (GpI) is well-known to be solvable in n^O(log n) time, but only recently has there been significant progress towards polynomial time. For example, in 2012 Babai et al. (ICALP 2012) gave a polynomial-time algorithm for groups with no abelian normal subgroups. ... more >>>

Joshua Grochow

We study the problem of matrix Lie algebra conjugacy. Lie algebras arise centrally in areas as diverse as differential equations, particle physics, group theory, and the Mulmuley--Sohoni Geometric Complexity Theory program. A matrix Lie algebra is a set $\mathcal{L}$ of matrices such that $A,B \in \mathcal{L}$ implies$AB - BA \in ... more >>>