A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z - Other

**G**

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TR24-070
| 10th April 2024
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Xinyu Mao, Guangxu Yang, Jiapeng Zhang#### Gadgetless Lifting Beats Round Elimination: Improved Lower Bounds for Pointer Chasing

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TR00-068
| 13th July 2000
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Peter Auer, Nicolo Cesa-Bianchi, Yoav Freund, Robert E. Schapire#### Gambling in a rigged casino: The adversarial multi-armed bandit problem

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TR15-149
| 8th September 2015
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Mohammad Hajiabadi, Bruce Kapron#### Gambling, Computational Information, and Encryption Security

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TR15-021
| 5th February 2015
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Stephen A. Fenner, Daniel Grier, Jochen Messner, Luke Schaeffer, Thomas Thierauf#### Game Values and Computational Complexity: An Analysis via Black-White Combinatorial Games

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TR24-053
| 10th March 2024
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Noam Mazor, Rafael Pass#### Gap MCSP is not (Levin) NP-complete in Obfustopia

Revisions: 1

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TR98-026
| 5th May 1998
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Richard Beigel#### Gaps in Bounded Query Hierarchies

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TR17-067
| 21st April 2017
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Benny Applebaum#### Garbled Circuits as Randomized Encodings of Functions: a Primer

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TR18-027
| 8th February 2018
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Jaroslaw Blasiok, Venkatesan Guruswami, Preetum Nakkiran, Atri Rudra, Madhu Sudan#### General Strong Polarization

Revisions: 1

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TR14-040
| 30th March 2014
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Hamed Hatami, Pooya Hatami, Shachar Lovett#### General systems of linear forms: equidistribution and true complexity

Revisions: 1

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TR08-027
| 4th December 2007
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Till Tantau#### Generalizations of the Hartmanis-Immerman-Sewelson Theorem and Applications to Infinite Subsets of P-Selective Sets

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TR05-142
| 1st December 2005
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Vadim Lyubashevsky, Daniele Micciancio#### Generalized Compact Knapsacks are Collision Resistant

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TR04-095
| 3rd November 2004
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Daniele Micciancio#### Generalized compact knapsacks, cyclic lattices, and efficient one-way functions from worst-case complexity assumptions

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TR18-074
| 23rd April 2018
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Daniel Kane, Shachar Lovett, Shay Moran#### Generalized comparison trees for point-location problems

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TR97-061
| 12th November 1997
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Eli Biham, Dan Boneh, Omer Reingold#### Generalized Diffie-Hellman Modulo a Composite is not Weaker than Factoring

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TR18-064
| 3rd April 2018
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Markus Bläser, Christian Ikenmeyer, Gorav Jindal, Vladimir Lysikov#### Generalized Matrix Completion and Algebraic Natural Proofs

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TR13-103
| 24th July 2013
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Gábor Ivanyos, Marek Karpinski, Youming Qiao, Miklos Santha#### Generalized Wong sequences and their applications to Edmonds' problems

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TR12-170
| 30th November 2012
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Scott Aaronson, Travis Hance#### Generalizing and Derandomizing Gurvits's Approximation Algorithm for the Permanent

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TR96-007
| 29th January 1996
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Miklos Ajtai#### Generating Hard Instances of Lattice Problems

Comments: 1

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TR13-185
| 24th December 2013
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Fu Li, Iddo Tzameret#### Generating Matrix Identities and Proof Complexity Lower Bounds

Revisions: 3

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TR04-037
| 14th April 2004
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Elmar Böhler, Christian Glaßer, Bernhard Schwarz, Klaus W. Wagner#### Generation Problems

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TR05-060
| 30th May 2005
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Philippe Moser#### Generic Density and Small Span Theorem

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TR05-162
| 23rd December 2005
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Yunlei Zhao, Jesper Buus Nielsen, Robert H. Deng, Feng Dengguo#### Generic yet Practical ZK Arguments from any Public-Coin HVZK

Revisions: 1

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TR19-060
| 18th April 2019
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Scott Aaronson, Guy Rothblum#### Gentle Measurement of Quantum States and Differential Privacy

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TR96-053
| 6th August 1996
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Yosi Ben-Asher, Ilan Newman#### Geometric Approach for Optimal Routing on Mesh with Buses

Revisions: 1

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TR20-029
| 6th March 2020
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Swastik Kopparty, Guy Moshkovitz, Jeroen Zuiddam#### Geometric Rank of Tensors and Subrank of Matrix Multiplication

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TR96-052
| 2nd October 1996
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Martin Dietzfelbinger#### Gossiping and Broadcasting versus Computing Functions in Networks

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TR05-116
| 12th October 2005
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Alex Samorodnitsky, Luca Trevisan#### Gowers Uniformity, Influence of Variables, and PCPs

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TR12-050
| 25th April 2012
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Avraham Ben-Aroya, Gil Cohen#### Gradual Small-Bias Sample Spaces

Revisions: 3

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

Revisions: 1

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TR10-050
| 25th March 2010
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Samir Datta, Prajakta Nimbhorkar, Thomas Thierauf, Fabian Wagner#### Graph Isomorphism for $K_{3,3}$-free and $K_5$-free graphs is in Log-space

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TR02-037
| 21st May 2002
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Vikraman Arvind, Piyush Kurur#### Graph Isomorphism is in SPP

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TR99-033
| 19th August 1999
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Vikraman Arvind, J. Köbler#### Graph Isomorphism is Low for ZPP$^{\mbox{\rm NP}}$ and other Lowness results.

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TR10-117
| 22nd July 2010
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Arkadev Chattopadhyay, Jacobo Toran, Fabian Wagner#### Graph Isomorphism is not AC^0 reducible to Group Isomorphism

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TR15-032
| 21st February 2015
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Vikraman Arvind, Johannes Köbler, Gaurav Rattan, Oleg Verbitsky#### Graph Isomorphism, Color Refinement, and Compactness

Revisions: 2

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TR11-077
| 8th May 2011
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Albert Atserias, Elitza Maneva#### Graph Isomorphism, Sherali-Adams Relaxations and Expressibility in Counting Logics

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TR98-075
| 9th December 1998
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Adam Klivans, Dieter van Melkebeek#### Graph Nonisomorphism has Subexponential Size Proofs Unless the Polynomial-Time Hierarchy Collapses.

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TR06-116
| 19th July 2006
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Amin Coja-Oghlan#### Graph partitioning via adaptive spectral techniques

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TR98-031
| 4th May 1998
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Dimitris Fotakis, Paul Spirakis#### Graph Properties that Facilitate Travelling

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TR99-047
| 10th November 1999
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Wolfgang Slany#### Graph Ramsey games

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TR14-121
| 22nd September 2014
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Sebastian Mueller#### Graph Structure and Parity Games

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TR11-032
| 11th March 2011
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Fabian Wagner#### Graphs of Bounded Treewidth can be Canonized in AC$^1$

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TR18-049
| 14th March 2018
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Stasys Jukna, Hannes Seiwert#### Greedy can also beat pure dynamic programming

Revisions: 1

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TR16-145
| 16th September 2016
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Markus Bläser, Gorav Jindal, Anurag Pandey#### Greedy Strikes Again: A Deterministic PTAS for Commutative Rank of Matrix Spaces

Revisions: 2

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TR10-151
| 30th September 2010
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Raghunath Tewari, N. V. Vinodchandran#### Green’s Theorem and Isolation in Planar Graphs

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TR05-149
| 7th December 2005
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Eric Allender, David Mix Barrington, Tanmoy Chakraborty, Samir Datta, Sambuddha Roy#### Grid Graph Reachability Problems

Revisions: 1

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TR14-073
| 14th May 2014
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Shachar Lovett, Cris Moore, Alexander Russell#### Group representations that resist random sampling

Revisions: 1

Xinyu Mao, Guangxu Yang, Jiapeng Zhang

The notion of query-to-communication lifting theorems is a generic framework to convert query lower bounds into two-party communication lower bounds. Though this framework is very generic and beautiful, it has some inherent limitations such as it only applies to lifted functions. In order to address this issue, we propose gadgetless ... more >>>

Peter Auer, Nicolo Cesa-Bianchi, Yoav Freund, Robert E. Schapire

In the multi-armed bandit problem, a gambler must decide which arm

of K non-identical slot machines to play in a sequence of trials

so as to maximize his reward.

This classical problem has received much attention because of the

simple model it provides of the trade-off between

exploration ...
more >>>

Mohammad Hajiabadi, Bruce Kapron

We revisit the question, originally posed by Yao (1982), of whether encryption security may be characterized using computational information. Yao provided an affirmative answer, using a compression-based notion of computational information to give a characterization equivalent to the standard computational notion of semantic security. We give two other equivalent characterizations. ... more >>>

Stephen A. Fenner, Daniel Grier, Jochen Messner, Luke Schaeffer, Thomas Thierauf

A black-white combinatorial game is a two-person game in which the pieces are colored either black or white. The players alternate moving or taking elements of a specific color designated to them before the game begins. A player loses the game if there is no legal move available for his ... more >>>

Noam Mazor, Rafael Pass

We demonstrate that under believable cryptographic hardness assumptions, Gap versions of standard meta-complexity problems, such as the Minimum Circuit Size problem (MCSP) and the Minimum Time-Bounded Kolmogorov Complexity problem (MKTP) are not NP-complete w.r.t. Levin (i.e., witness-preserving many-to-one) reductions.

In more detail:

- Assuming the existence of indistinguishability obfuscation, and ...
more >>>

Richard Beigel

<html>

Prior results show that most bounded query hierarchies cannot

contain finite gaps. For example, it is known that

<center>

P<sub>(<i>m</i>+1)-tt</sub><sup>SAT</sup> = P<sub><i>m</i>-tt</sub><sup>SAT</sup> implies P<sub>btt</sub><sup>SAT</sup> = P<sub><i>m</i>-tt</sub><sup>SAT</sup>

</center>

and for all sets <i>A</i>

<ul>

<li> FP<sub>(<i>m</i>+1)-tt</sub><sup><i>A</i></sup> = FP<sub><i>m</i>-tt</sub><sup><i>A</i></sup> implies FP<sub>btt</sub><sup><i>A</i></sup> = FP<sub><i>m</i>-tt</sub><sup><i>A</i></sup>

</li>

<li> P<sub>(<i>m</i>+1)-T</sub><sup><i>A</i></sup> = P<sub><i>m</i>-T</sub><sup><i>A</i></sup> implies P<sub>bT</sub><sup><i>A</i></sup> = ...
more >>>

Benny Applebaum

Yao's garbled circuit construction is a central cryptographic tool with numerous applications. In this tutorial, we study garbled circuits from a foundational point of view under the framework of \emph{randomized encoding} (RE) of functions. We review old and new constructions of REs, present some lower bounds, and describe some applications. ... more >>>

Jaroslaw Blasiok, Venkatesan Guruswami, Preetum Nakkiran, Atri Rudra, Madhu Sudan

Ar\i kan's exciting discovery of polar codes has provided an altogether new way to efficiently achieve Shannon capacity. Given a (constant-sized) invertible matrix $M$, a family of polar codes can be associated with this matrix and its ability to approach capacity follows from the $\textit{polarization}$ of an associated $[0,1]$-bounded martingale, ... more >>>

Hamed Hatami, Pooya Hatami, Shachar Lovett

The densities of small linear structures (such as arithmetic progressions) in subsets of Abelian groups can be expressed as certain analytic averages involving linear forms. Higher-order Fourier analysis examines such averages by approximating the indicator function of a subset by a function of bounded number of polynomials. Then, to approximate ... more >>>

Till Tantau

The Hartmanis--Immerman--Sewelson theorem is the classical link between the exponential and the polynomial time realm. It states that NE = E if, and only if, every sparse set in NP lies in P. We establish similar links for classes other than sparse sets:

1. E = UE if, and only ... more >>>

Vadim Lyubashevsky, Daniele Micciancio

The generalized knapsack problem is the following: given $m$ random

elements $a_1,\ldots,a_m\in R$ for some ring $R$, and a target $t\in

R$, find elements $z_1,\ldots,z_m\in D$ such that $\sum{a_iz_i}=t$

where $D$ is some given subset of $R$. In (Micciancio, FOCS 2002),

it was proved that for appropriate choices of $R$ ...
more >>>

Daniele Micciancio

We investigate the average case complexity of a generalization of the compact knapsack problem to arbitrary rings: given $m$ (random) ring elements a_1,...,a_m in R and a (random) target value b in R, find coefficients x_1,...,x_m in S (where S is an appropriately chosen subset of R) such that a_1*x_1 ... more >>>

Daniel Kane, Shachar Lovett, Shay Moran

Let $H$ be an arbitrary family of hyper-planes in $d$-dimensions. We show that the point-location problem for $H$

can be solved by a linear decision tree that only uses a special type of queries called \emph{generalized comparison queries}. These queries correspond to hyperplanes that can be written as a linear ...
more >>>

Eli Biham, Dan Boneh, Omer Reingold

The Diffie-Hellman key-exchange protocol may naturally be

extended to k>2 parties. This gives rise to the generalized

Diffie-Hellman assumption (GDH-Assumption).

Naor and Reingold have recently shown an efficient construction

of pseudo-random functions and reduced the security of their

construction to the GDH-Assumption.

In this note, we ...
more >>>

Markus Bläser, Christian Ikenmeyer, Gorav Jindal, Vladimir Lysikov

Algebraic natural proofs were recently introduced by Forbes, Shpilka and Volk (Proc. of the 49th Annual {ACM} {SIGACT} Symposium on Theory of Computing (STOC), pages {653--664}, 2017) and independently by Grochow, Kumar, Saks and Saraf~(CoRR, abs/1701.01717, 2017) as an attempt to transfer Razborov and Rudich's famous barrier result (J. Comput. ... more >>>

Gábor Ivanyos, Marek Karpinski, Youming Qiao, Miklos Santha

We design two deterministic polynomial time algorithms for variants of a problem introduced by Edmonds in 1967: determine the rank of a matrix $M$ whose entries are homogeneous linear polynomials over the integers. Given a linear subspace $\mathcal{B}$ of the $n \times n$ matrices over some field $\mathbb{F}$, we consider ... more >>>

Scott Aaronson, Travis Hance

Around 2002, Leonid Gurvits gave a striking randomized algorithm to approximate the permanent of an n×n matrix A. The algorithm runs in O(n^2/?^2) time, and approximates Per(A) to within ±?||A||^n additive error. A major advantage of Gurvits's algorithm is that it works for arbitrary matrices, not just for nonnegative matrices. ... more >>>

Miklos Ajtai

We give a random class of n dimensional lattices so that, if

there is a probabilistic polynomial time algorithm which finds a short

vector in a random lattice with a probability of at least 1/2

then there is also a probabilistic polynomial time algorithm which

solves the following three ...
more >>>

Fu Li, Iddo Tzameret

Motivated by the fundamental lower bounds questions in proof complexity, we investigate the complexity of generating identities of matrix rings, and related problems. Specifically, for a field $\mathbb{F}$ let $A$ be a non-commutative (associative) $\mathbb{F}$-algebra (e.g., the algebra Mat$_d(\mathbb{F})\;$ of $d\times d$ matrices over $\mathbb{F}$). We say that a non-commutative ... more >>>

Elmar Böhler, Christian Glaßer, Bernhard Schwarz, Klaus W. Wagner

Given a fixed computable binary operation f, we study the complexity of the following generation problem: The input consists of strings a1,...,an,b. The question is whether b is in the closure of {a1,...,an} under operation f.

For several subclasses of operations we prove tight upper and lower bounds for the ... more >>>

Philippe Moser

We refine the genericity concept of Ambos-Spies et al, by assigning a real number in $[0,1]$ to every generic set, called its generic density.

We construct sets of generic density any E-computable real in $[0,1]$.

We also introduce strong generic density, and show that it is related to packing ...
more >>>

Yunlei Zhao, Jesper Buus Nielsen, Robert H. Deng, Feng Dengguo

In this work, we present a generic yet practical transformation from any public-coin honest-verifier zero-knowledge (HVZK) protocols to normal zero-knowledge (ZK) arguments. By ``generic", we mean that the transformation is applicable to any public-coin HVZK protocol under any one-way function (OWF) admitting Sigma-protocols. By ``practical" we mean that the transformation ... more >>>

Scott Aaronson, Guy Rothblum

In differential privacy (DP), we want to query a database about $n$ users, in a way that "leaks at most $\varepsilon$ about any individual user," even conditioned on any outcome of the query. Meanwhile, in gentle measurement, we want to measure $n$ quantum states, in a way that "damages the ... more >>>

Yosi Ben-Asher, Ilan Newman

The architecture of 'mesh of buses' is an important model in parallel computing. Its main advantage is that the additional broadcast capability can be used to overcome the main disadvantage of the mesh, namely its relatively large diameter. We show that the addition of buses indeed accelerates routing times. Furthermore, ... more >>>

Swastik Kopparty, Guy Moshkovitz, Jeroen Zuiddam

Motivated by problems in algebraic complexity theory (e.g., matrix multiplication) and extremal combinatorics (e.g., the cap set problem and the sunflower problem), we introduce the geometric rank as a new tool in the study of tensors and hypergraphs. We prove that the geometric rank is an upper bound on the ... more >>>

Martin Dietzfelbinger

The fundamental assumption in the classical theory of

dissemination of information in interconnection networks

(gossiping and broadcasting) is that atomic pieces of information

are communicated. We show that, under suitable assumptions about

the way processors may communicate, computing an n-ary function

that has a "critical input" (e.g., ...
more >>>

Alex Samorodnitsky, Luca Trevisan

Gowers introduced, for d\geq 1, the notion of dimension-d uniformity U^d(f)

of a function f: G -> \C, where G is a finite abelian group and \C are the

complex numbers. Roughly speaking, if a function has small Gowers uniformity

of dimension d, then it ``looks random'' on ...
more >>>

Avraham Ben-Aroya, Gil Cohen

A $(k,\epsilon)$-biased sample space is a distribution over $\{0,1\}^n$ that $\epsilon$-fools every nonempty linear test of size at most $k$. Since they were introduced by Naor and Naor [SIAM J. Computing, 1993], these sample spaces have become a central notion in theoretical computer science with a variety of applications.

When ... 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 >>>

Samir Datta, Prajakta Nimbhorkar, Thomas Thierauf, Fabian Wagner

Graph isomorphism is an important and widely studied computational problem, with

a yet unsettled complexity.

However, the exact complexity is known for isomorphism of various classes of

graphs. Recently [DLN$^+$09] proved that planar graph isomorphism is complete for log-space.

We extend this result of [DLN$^+$09] further

to the ...
more >>>

Vikraman Arvind, Piyush Kurur

We show that Graph Isomorphism is in the complexity class

SPP, and hence it is in $\ParityP$ (in fact, it is in $\ModkP$ for

each $k\geq 2$). We derive this result as a corollary of a more

general result: we show that a {\em generic problem} $\FINDGROUP$ has

an $\FP^{\SPP}$ ...
more >>>

Vikraman Arvind, J. Köbler

We show the following new lowness results for the probabilistic

class ZPP$^{\mbox{\rm NP}}$.

1. The class AM$\cap$coAM is low for ZPP$^{\mbox{\rm NP}}$.

As a consequence it follows that Graph Isomorphism and several

group-theoretic problems known to be in AM$\cap$coAM are low for

ZPP$^{\mbox{\rm ...
more >>>

Arkadev Chattopadhyay, Jacobo Toran, Fabian Wagner

We give a new upper bound for the Group and Quasigroup

Isomorphism problems when the input structures

are given explicitly by multiplication tables. We show that these problems can be computed by polynomial size nondeterministic circuits of unbounded fan-in with $O(\log\log n)$ depth and $O(\log^2 n)$ nondeterministic bits, ...
more >>>

Vikraman Arvind, Johannes Köbler, Gaurav Rattan, Oleg Verbitsky

Color refinement is a classical technique used to show that two given graphs $G$ and $H$

are non-isomorphic; it is very efficient, although it does not succeed on all graphs. We call a graph $G$ amenable to color refinement if the color-refinement procedure succeeds in distinguishing $G$ from any non-isomorphic ...
more >>>

Albert Atserias, Elitza Maneva

Two graphs with adjacency matrices $\mathbf{A}$ and $\mathbf{B}$ are isomorphic if there exists a permutation matrix $\mathbf{P}$ for which the identity $\mathbf{P}^{\mathrm{T}} \mathbf{A} \mathbf{P} = \mathbf{B}$ holds. Multiplying through by $\mathbf{P}$ and relaxing the permutation matrix to a doubly stochastic matrix leads to the notion of fractional isomorphism. We show ... more >>>

Adam Klivans, Dieter van Melkebeek

We establish hardness versus randomness trade-offs for a

broad class of randomized procedures. In particular, we create efficient

nondeterministic simulations of bounded round Arthur-Merlin games using

a language in exponential time that cannot be decided by polynomial

size oracle circuits with access to satisfiability. We show that every

language with ...
more >>>

Amin Coja-Oghlan

We study the use of spectral techniques for graph partitioning. Let G=(V,E) be a graph whose vertex set has a ``latent'' partition V_1,...,V_k. Moreover, consider a ``density matrix'' E=(E_vw)_{v,w in V} such that for v in V_i and w in V_j the entry E_{vw} is the fraction of all possible ... more >>>

Dimitris Fotakis, Paul Spirakis

In this work, we study two special cases of the metric Travelling Salesman

Problem, Graph TSP and TSP(1,2). At first, we show that dense instances of

TSP(1,2) and Graph TSP are essentially as hard to approximate as general

instances of TSP(1,2).

Next, we present an NC algorithm for TSP(1,2) that ... more >>>

Wolfgang Slany

We consider combinatorial avoidance and achievement games

based on graph Ramsey theory: The players take turns in coloring

still uncolored edges of a graph G, each player being assigned a

distinct color, choosing one edge per move. In avoidance games,

completing a monochromatic subgraph isomorphic to ...
more >>>

Sebastian Mueller

We investigate the possible structural changes one can perform on a game graph without destroying the winning regions of the players playing a parity game on it. More precisely, given a game graph $(G,p)$ for which we can efficiently compute winning regions, can we remove or add a vertex or ... more >>>

Fabian Wagner

In recent results the complexity of isomorphism testing on

graphs of bounded treewidth is improved to TC$^1$ [GV06] and further to LogCFL [DTW10].

The computation of canonical forms or a canonical labeling provides more information than

isomorphism testing.

Whether canonization is in NC or even TC$^1$ was stated ...
more >>>

Stasys Jukna, Hannes Seiwert

Many dynamic programming algorithms are ``pure'' in that they only use min or max and addition operations in their recursion equations. The well known greedy algorithm of Kruskal solves the minimum weight spanning tree problem on $n$-vertex graphs using only $O(n^2\log n)$ operations. We prove that any pure DP algorithm ... more >>>

Markus Bläser, Gorav Jindal, Anurag Pandey

We consider the problem of commutative rank computation of a given matrix space, $\mathcal{B}\subseteq\mathbb{F}^{n\times n}$. The problem is fundamental, as it generalizes several computational problems from algebra and combinatorics. For instance, checking if the commutative rank of the space is $n$, subsumes problems such as testing perfect matching in graphs ... more >>>

Raghunath Tewari, N. V. Vinodchandran

We show a simple application of Green’s theorem from multivariable calculus to the isolation problem in planar graphs. In particular, we construct a skew-symmetric, polynomially bounded, edge weight function for a directed planar graph in logspace such that the weight of any simple cycle in the graph is non-zero with ... more >>>

Eric Allender, David Mix Barrington, Tanmoy Chakraborty, Samir Datta, Sambuddha Roy

We study the complexity of restricted versions of st-connectivity, which is the standard complete problem for NL. Grid graphs are a useful tool in this regard, since

* reachability on grid graphs is logspace-equivalent to reachability in general planar digraphs, and

* reachability on certain classes of grid graphs gives ...
more >>>

Shachar Lovett, Cris Moore, Alexander Russell

We show that there exists a family of groups $G_n$ and nontrivial irreducible representations $\rho_n$ such that, for any constant $t$, the average of $\rho_n$ over $t$ uniformly random elements $g_1, \ldots, g_t \in G_n$ has operator norm $1$ with probability approaching 1 as $n \rightarrow \infty$. More quantitatively, we ... more >>>