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2011 IEEE 26th Annual Conference on Computational Complexity

8-11 June 2011

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  • [Front cover]

    Publication Year: 2011, Page(s): C1
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  • [Title page i]

    Publication Year: 2011, Page(s): i
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  • [Title page iii]

    Publication Year: 2011, Page(s): iii
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  • [Copyright notice]

    Publication Year: 2011, Page(s): iv
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  • Table of contents

    Publication Year: 2011, Page(s):v - vii
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  • Preface

    Publication Year: 2011, Page(s): viii
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  • Program Committee

    Publication Year: 2011, Page(s): ix
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  • Steering Committee

    Publication Year: 2011, Page(s): x
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  • Reviewers

    Publication Year: 2011, Page(s): xi
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  • Best Paper awards

    Publication Year: 2011, Page(s): xii
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  • Improved Direct Product Theorems for Randomized Query Complexity

    Publication Year: 2011, Page(s):1 - 11
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (469 KB) | HTML iconHTML

    The "direct product problem" is a fundamental question in complexity theory which seeks to understand how the difficulty of computing a function on each of k independent inputs scales with k. We prove the following direct product theorem (DPT) for query complexity: if every T-query algorithm has success probability at most 1 - ε in computing the Boolean function f on input distribution �... View full abstract»

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  • Making Branching Programs Oblivious Requires Superlogarithmic Overhead

    Publication Year: 2011, Page(s):12 - 22
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (402 KB) | HTML iconHTML

    We prove a time-space tradeoff lower bound of T = Ω (n log(n/s) log log(n/s)) for randomized oblivious branching programs to compute 1GAP, also known as the pointer jumping problem, a problem for which there is a simple deterministic time n and space O(log n) RAM (random access machine) algorithm. We give a similar time-space tradeoff of T = Ω (n log(n/s) log log(n/s)) for Boolean ra... View full abstract»

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  • Hardness of Max-2Lin and Max-3Lin over Integers, Reals, and Large Cyclic Groups

    Publication Year: 2011, Page(s):23 - 33
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (316 KB) | HTML iconHTML

    In 1997, Hastad showed NP-hardness of (1 - ε, 1/q + δ)-approximating Max-3Lin(Zq); however it was not until 2007 that Guruswami and Raghavendra were able to show NP-hardness of (1 - ε, δ)- approximating Max-3Lin(Z). In 2004, Khot-Kindler-Mossel-O'Donnell showed UG-hardness of (1 - ε, δ) approximating Max-2Lin(Zq) for q = q(ε, &... View full abstract»

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  • Lower Bounds on Query Complexity for Testing Bounded-Degree CSPs

    Publication Year: 2011, Page(s):34 - 44
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (267 KB) | HTML iconHTML

    In this paper, we consider lower bounds on the query complexity for testing CSPs in the bounded-degree model. We mainly consider Boolean CSPs allowing literals. First, for any "symmetric" predicate P : {0, 1}k → {0,1} except EQU where k ≥ 3, we show that every (randomized) algorithm that distinguishes satisfiable instances of CSP(P) from instances (|P-1 (0)|/2... View full abstract»

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  • Non-negatively Weighted #CSP: An Effective Complexity Dichotomy

    Publication Year: 2011, Page(s):45 - 54
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (279 KB) | HTML iconHTML

    We prove a complexity dichotomy theorem for all non-negatively weighted counting Constraint Satisfaction Problems (#CSP). This caps a long series of important results on counting problems, including unweighted and weighted graph homomorphisms and the celebrated dichotomy theorem for unweighted #CSP. Our dichotomy theorem gives a succinct criterion for tractability. If a set F of constraint functio... View full abstract»

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  • Symmetric LDPC Codes are not Necessarily Locally Testable

    Publication Year: 2011, Page(s):55 - 65
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (311 KB) | HTML iconHTML

    Locally testable codes, i.e., codes where membership in the code is testable with a constant number of queries, have played a central role in complexity theory. It is well known that a code must be a "low-density parity check'' (LDPC) code for it to be locally testable, but few LDPC codes are known to be locally testable, and even fewer classes of LDPC codes are known not to be locally testable. I... View full abstract»

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  • Towards Lower Bounds on Locally Testable Codes via Density Arguments

    Publication Year: 2011, Page(s):66 - 76
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (281 KB) | HTML iconHTML

    The main open problem in the area of locally testable codes (LTCs) is whether there exists an asymptotically good family of LTCs and to resolve this question it suffices to consider the case of query complexity 3. We argue that to refute the existence of such an asymptotically good family one should prove that the number of dual codewords of weight at most 3 is super-linear in the blocklength of t... View full abstract»

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  • Linear-Algebraic List Decoding of Folded Reed-Solomon Codes

    Publication Year: 2011, Page(s):77 - 85
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (270 KB) | HTML iconHTML

    Folded Reed-Solomon codes are an explicit family of codes that achieve the optimal trade-off between rate and error-correction capability: specifically, for any ε >; 0, the author and Rudra (2006, 08) presented an nO(1/ε) time algorithm to list decode appropriate folded RS codes of rate R from a fraction 1-R-ε of errors. The algorithm is based on multivariate pol... View full abstract»

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  • Noisy Interpolation of Sparse Polynomials, and Applications

    Publication Year: 2011, Page(s):86 - 92
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (265 KB) | HTML iconHTML

    Let f ∈Fq [x] be a polynomial of degree d ≤ q/2. It is well-known that f can be uniquely recovered from its values at some 2d points even after some small fraction of the values are corrupted. In this paper we establish a similar result for sparse polynomials. We show that a k-sparse polynomial f ∈Fq [x] of degree d ≤ q/2 can be recovered from its ... View full abstract»

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  • Paris-Harrington Tautologies

    Publication Year: 2011, Page(s):93 - 103
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (453 KB) | HTML iconHTML

    We study the proof complexity of Paris-Harrington's Large Ramsey Theorem for bi-colorings of graphs. We prove a non-trivial conditional lower bound in Resolution and a quasi-polynomial upper bound in bounded-depth Frege. The lower bound is conditional on a (very reasonable) hardness assumption for a weak (quasi-polynomial) Pigeonhole principle in RES(2). We show that under such assumption, there i... View full abstract»

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  • Relativized Separations of Worst-Case and Average-Case Complexities for NP

    Publication Year: 2011, Page(s):104 - 114
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (299 KB) | HTML iconHTML

    Non-relativization of complexity issues can be interpreted as showing that these issues cannot be resolved by "black-box" techniques. We show that the assumption DistNP ⊆ AvgP does not imply that NP ⊆ BPP by relativizing techniques. More precisely, we give an oracle relative to which the assumption holds but the conclusion fails. Moreover, relative to our oracle, there are problems i... View full abstract»

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  • Non-uniform ACC Circuit Lower Bounds

    Publication Year: 2011, Page(s):115 - 125
    Cited by:  Papers (17)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (444 KB) | HTML iconHTML

    The class ACC consists of circuit families with constant depth over unbounded fan-in AND, OR, NOT, and MODm gates, where m >; 1 is an arbitrary constant. We prove: 1. NTIME[2n] does not have non-uniform ACC circuits of polynomial size. The size lower bound can be strengthened to quasi-polynomials and other less natural functions. 2. ENP, the class of languages recognized i... View full abstract»

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  • Improved Constructions of Three Source Extractors

    Publication Year: 2011, Page(s):126 - 136
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (441 KB) | HTML iconHTML

    We study the problem of constructing extractors for independent weak random sources. The probabilistic method shows that there exists an extractor for two independent weak random sources on n bits with only logarithmic min-entropy. However, previously the best known explicit two source extractor only achieves min-entropy 0.499n, and the best known three source extractor only achieves min-entropy n... View full abstract»

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  • A New Approach to Affine Extractors and Dispersers

    Publication Year: 2011, Page(s):137 - 147
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (406 KB) | HTML iconHTML

    We study the problem of constructing affine extractors over GF(2). Previously the only known construction that can handle sources with arbitrarily linear entropy is due to Bourgain (and a slight modification by Yehudayoff), which makes extensive use of complicated inequality manipulations and relies on a careful choice of a polynomial. In this paper we give a new and conceptually much cleaner cons... View full abstract»

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  • Symmetry of Information and Bounds on Nonuniform Randomness Extraction via Kolmogorov Extractors

    Publication Year: 2011, Page(s):148 - 156
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (415 KB) | HTML iconHTML

    We prove a strong Symmetry of Information relation for random strings (in the sense of Kolmogorov complexity) and establish tight bounds on the amount on nonuniformity that is necessary for extracting a string with randomness rate 1 from a single source of randomness. More precisely, as instantiations of more general results, we show: · For all n-bit random strings x and y, x is random cond... View full abstract»

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