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1
June 2015
CCC '15: Proceedings of the 30th Conference on Computational Complexity
Publisher: Schloss DagstuhlLeibnizZentrum fuer Informatik
We continue the study of covering complexity of constraint satisfaction problems (CSPs) initiated by Guruswami, Håstad and Sudan [9] and Dinur and Kol [7]. The covering number of a CSP instance Φ, denoted by ν (Φ) is the smallest number of assignments to the variables of Φ, such that each ...
Keywords:
CSPs, unique games, covering problem, hardness of approximation, invariance principle
2
June 2015
STOC '15: Proceedings of the fortyseventh annual ACM symposium on Theory of computing
Publisher: ACM
Bibliometrics:
Citation Count: 0
Downloads (6 Weeks): 3, Downloads (12 Months): 27, Downloads (Overall): 68
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We show that every language in NP has a PCP verifier that tosses O(log n) random coins, has perfect completeness, and a soundness error of at most 1/poly(n), while making O(poly log log n) queries into a proof over an alphabet of size at most n 1/poly log log n ...
Keywords:
sliding scale conjecture, PCPs, composition, decodable PCPs
3
May 2014
STOC '14: Proceedings of the fortysixth annual ACM symposium on Theory of computing
Publisher: ACM
Bibliometrics:
Citation Count: 4
Downloads (6 Weeks): 4, Downloads (12 Months): 15, Downloads (Overall): 81
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We prove improved inapproximability results for hypergraph coloring using the lowdegree polynomial code (aka, the"short code" of Barak et. al . [FOCS 2012]) and the techniques proposed by Dinur and Guruswami [FOCS 2013] to incorporate this code for inapproximability results. In particular, we prove quasiNPhardness of the following problems on ...
Keywords:
hardness of approximation, hypergraph coloring, short code
4
January 2013
Journal of the ACM (JACM): Volume 59 Issue 6, December 2012
Publisher: ACM
Bibliometrics:
Citation Count: 2
Downloads (6 Weeks): 3, Downloads (12 Months): 20, Downloads (Overall): 294
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Let X be randomly chosen from {1,1} n , and let Y be randomly chosen from the standard spherical Gaussian on ℝ n . For any (possibly unbounded) polytope P formed by the intersection of k halfspaces, we prove that Pr[ X ∈ P ]  Pr[ Y ∈ P ...
Keywords:
polytopes, intersection of halfspaces, pseudorandomness, agnostic learning, noise sensitivity, Invariance
5
June 2011
STOC '11: Proceedings of the fortythird annual ACM symposium on Theory of computing
Publisher: ACM
Bibliometrics:
Citation Count: 3
Downloads (6 Weeks): 1, Downloads (12 Months): 13, Downloads (Overall): 282
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In this paper, we study the complexity of computing the determinant of a matrix over a noncommutative algebra. In particular, we ask the question: "Over which algebras is the determinant easier to compute than the permanent?" Towards resolving this question, we show the following results for noncommutative determinant computation: [Hardness] ...
Keywords:
computational algebra, determinant, noncommutative algebras, permanent
6
June 2010
STOC '10: Proceedings of the fortysecond ACM symposium on Theory of computing
Publisher: ACM
Bibliometrics:
Citation Count: 4
Downloads (6 Weeks): 0, Downloads (12 Months): 6, Downloads (Overall): 143
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Let X be randomly chosen from {1,1} n , and let Y be randomly chosen from the standard spherical Gaussian on R n . For any (possibly unbounded) polytope P formed by the intersection of k halfspaces, we prove that Pr[X ∈ P]  Pr[Y ∈ P] ≤ log 8/5 ...
Keywords:
agnostic learning, average sensitivity, contingency tables, invariance principles, limit theorems, noise sensitivity, polytopes, pseudorandom generators
7
June 2010
STOC '10: Proceedings of the fortysecond ACM symposium on Theory of computing
Publisher: ACM
Bibliometrics:
Citation Count: 11
Downloads (6 Weeks): 1, Downloads (12 Months): 9, Downloads (Overall): 226
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We give the first nontrivial upper bounds on the average sensitivity and noise sensitivity of degreed polynomial threshold functions (PTFs). These bounds hold both for PTFs over the Boolean hypercube {1,1} n and for PTFs over R n under the standard ndimensional Gaussian distribution N(0,I n ). Our bound on ...
Keywords:
average sensitivity, boolean function, fourier analysis, noise sensitivity, polynomial threshold function
8
May 2010
ACM Transactions on Computational Logic (TOCL): Volume 11 Issue 3, May 2010
Publisher: ACM
Bibliometrics:
Citation Count: 1
Downloads (6 Weeks): 1, Downloads (12 Months): 2, Downloads (Overall): 143
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We present a simple proof of the boundeddepth Frege proof lower bounds of Pitassi et al. [1993] and Krajíček et al. [1995] for the pigeonhole principle. Our method uses the interpretation of proofs as two player games given by Pudlák and Buss. Our lower bound is conceptually simpler than previous ...
Keywords:
Frege proofs, Proof complexity, lower bounds, pigeonhole principle
9
January 2010
IEEE Transactions on Information Theory: Volume 56 Issue 1, January 2010
Publisher: IEEE Press
Let X and Y be finite nonempty sets and (X,Y) a pair of random variables taking values in X × Y . We consider communication protocols between two parties, ALICE and BOB, for generating X and Y . ALICE is provided an x ∈ X generated according to the distribution ...
Keywords:
direct sum, mutual information, relative entropy, Communication complexity, communication complexity, rejection sampling
10
January 2010
Property testing: current research and surveys
Publisher: SpringerVerlag
The main result of this paper is a generic composition theorem for low error twoquery probabilistically checkable proofs (PCPs). Prior to this work, composition of PCPs was wellunderstood only in the constant error regime. Existing composition methods in the low error regime were nonmodular (i.e., very much tailored to the ...
Keywords:
PCP, locally decodable, low soundness error, composition
11
January 2010
Property testing: current research and surveys
Publisher: SpringerVerlag
The main result of this paper is a generic composition theorem for low error twoquery probabilistically checkable proofs (PCPs). Prior to this work, composition of PCPs was wellunderstood only in the constant error regime. Existing composition methods in the low error regime were nonmodular (i.e., very much tailored to the ...
Keywords:
low soundness error, composition, PCP, locally decodable
12
October 2009
FOCS '09: Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Publisher: IEEE Computer Society
The main result of this paper is a generic composition theorem for low error twoquery probabilistically checkable proofs (PCPs). Prior to this work, composition of PCPs was wellunderstood only in the constant error regime. Existing composition methods in the low error regime were nonmodular (i.e., very much tailored to the ...
Keywords:
PCP, composition, locally decodable, low soundness error
13
September 2009
ACM Transactions on Computation Theory (TOCT): Volume 1 Issue 2, September 2009
Publisher: ACM
Bibliometrics:
Citation Count: 3
Downloads (6 Weeks): 2, Downloads (12 Months): 7, Downloads (Overall): 229
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We initiate the study of the tradeoff between the length of a probabilistically checkable proof of proximity (PCPP) and the maximal soundness that can be guaranteed by a 3query verifier with oracle access to the proof. Our main observation is that a verifier limited to querying a short proof cannot ...
Keywords:
PCP, PCP of proximity
14
July 2008
UAI'08: Proceedings of the TwentyFourth Conference on Uncertainty in Artificial Intelligence
Publisher: AUAI Press
It is wellknown that inference in graphical models is hard in the worst case, but tractable for models with bounded treewidth. We ask whether treewidth is the only structural criterion of the underlying graph that enables tractable inference. In other words, is there some class of structures with unbounded treewidth ...
15
July 2008
ICALP '08: Proceedings of the 35th international colloquium on Automata, Languages and Programming  Volume Part I
Publisher: SpringerVerlag
We initiate the study of the tradeoff between the length of a probabilistically checkable proof of proximity (PCPP) and the maximal soundness that can be guaranteed by a 3query verifier with oracle access to the proof. Our main observation is that a verifier limited to querying a short proof cannot ...
16
January 2008
SODA '08: Proceedings of the nineteenth annual ACMSIAM symposium on Discrete algorithms
Publisher: Society for Industrial and Applied Mathematics
Bibliometrics:
Citation Count: 8
Downloads (6 Weeks): 0, Downloads (12 Months): 2, Downloads (Overall): 250
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We consider the problem of minimizing average latency cost while obliviously routing traffic in a network with linear latency functions. This is roughly equivalent to minimizing the function Σ e (load( e )) 2 , where for a network link e , load( e ) denotes the amount of traffic ...
17
June 2007
CCC '07: Proceedings of the TwentySecond Annual IEEE Conference on Computational Complexity
Publisher: IEEE Computer Society
We examine the communication required for generating random variables remotely. One party Alice is given a distribution D, and she has to send a message to Bob, who is then required to generate a value with distribution exactly D. Alice and Bob are allowed to share random bits generated without ...
18
May 2007
Computational Complexity: Volume 16 Issue 1, May 2007
Publisher: Birkhauser Verlag
We initiate a study of tradeoffs between communication and computation in wellknown communication models and in other related models. The fundamental question we investigate is the following: Is there a computational task that exhibits a strong tradeoff behavior between the amount of communication and the amount of time needed for ...
Keywords:
68Q15, 68Q17, computation, tradeoffs, Communication complexity
19
December 2006
SIAM Journal on Computing: Volume 36 Issue 4, December 2006
Publisher: Society for Industrial and Applied Mathematics
We continue the study of the tradeoff between the length of probabilistically checkable proofs (PCPs) and their query complexity, establishing the following main results (which refer to proofs of satisfiability of circuits of size $n$): 1. We present PCPs of length $\exp(o(\log\log n)^2)\cdot n$ that can be verified by making ...
Keywords:
probabilistically checkable proofs, locally decodable codes, locally testable codes, PCP, property testing
20
July 2005
SIAM Journal on Computing: Volume 35 Issue 1, 2005
Publisher: Society for Industrial and Applied Mathematics
For a Boolean formula $\phi$ on n variables, the associated property $P_\phi$ is the collection of n bit strings that satisfy $\phi$. We study the query complexity of tests that distinguish (with high probability) between strings in $P_\phi$ and strings that are far from $P_\phi$ in Hamming distance. We prove ...
Keywords:
lower bounds, locally testable codes, CNF formulae, property testing, sublinear algorithms

