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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 forty-seventh annual ACM symposium on Theory of computing Publisher: ACM Bibliometrics: Citation Count: 0 Downloads (6 Weeks): 3,   Downloads (12 Months): 27,   Downloads (Overall): 68 Full text available: PDF 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 forty-sixth annual ACM symposium on Theory of computing Publisher: ACM Bibliometrics: Citation Count: 4 Downloads (6 Weeks): 4,   Downloads (12 Months): 15,   Downloads (Overall): 81 Full text available: PDF We prove improved inapproximability results for hypergraph coloring using the low-degree 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 quasi-NP-hardness 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 Full text available: PDF 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 forty-third annual ACM symposium on Theory of computing Publisher: ACM Bibliometrics: Citation Count: 3 Downloads (6 Weeks): 1,   Downloads (12 Months): 13,   Downloads (Overall): 282 Full text available: PDF 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 forty-second ACM symposium on Theory of computing Publisher: ACM Bibliometrics: Citation Count: 4 Downloads (6 Weeks): 0,   Downloads (12 Months): 6,   Downloads (Overall): 143 Full text available: PDF 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 forty-second ACM symposium on Theory of computing Publisher: ACM Bibliometrics: Citation Count: 11 Downloads (6 Weeks): 1,   Downloads (12 Months): 9,   Downloads (Overall): 226 Full text available: PDF We give the first non-trivial upper bounds on the average sensitivity and noise sensitivity of degree-d 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 n-dimensional 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 Full text available: PDF We present a simple proof of the bounded-depth 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 Bibliometrics: Citation Count: 12 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: Springer-Verlag Bibliometrics: Citation Count: 2 The main result of this paper is a generic composition theorem for low error two-query probabilistically checkable proofs (PCPs). Prior to this work, composition of PCPs was well-understood only in the constant error regime. Existing composition methods in the low error regime were non-modular (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: Springer-Verlag Bibliometrics: Citation Count: 0 The main result of this paper is a generic composition theorem for low error two-query probabilistically checkable proofs (PCPs). Prior to this work, composition of PCPs was well-understood only in the constant error regime. Existing composition methods in the low error regime were non-modular (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 Bibliometrics: Citation Count: 10 The main result of this paper is a generic composition theorem for low error two-query probabilistically checkable proofs (PCPs). Prior to this work, composition of PCPs was well-understood only in the constant error regime. Existing composition methods in the low error regime were non-modular (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 Full text available: PDF We initiate the study of the trade-off between the length of a probabilistically checkable proof of proximity (PCPP) and the maximal soundness that can be guaranteed by a 3-query 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 Twenty-Fourth Conference on Uncertainty in Artificial Intelligence Publisher: AUAI Press Bibliometrics: Citation Count: 3 It is well-known 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: Springer-Verlag Bibliometrics: Citation Count: 4 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 3-query 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 ACM-SIAM 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 Full text available: PDF 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 Twenty-Second Annual IEEE Conference on Computational Complexity Publisher: IEEE Computer Society Bibliometrics: Citation Count: 18 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 Bibliometrics: Citation Count: 0 We initiate a study of tradeoffs between communication and computation in well-known 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 Bibliometrics: Citation Count: 41 We continue the study of the trade-off 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 Bibliometrics: Citation Count: 53 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