21st Annual IEEE Conference on Computational Complexity (CCC'06)

16-20 July 2006

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  • Proceedings. Twenty-First Annual IEEE Conference on Computational Complexity

    Publication Year: 2006, Page(s): c1
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  • 21st Annual IEEE Conference on Computational Complexity - Title

    Publication Year: 2006, Page(s):i - iii
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  • 21st Annual IEEE Conference on Computational Complexity - Copyright

    Publication Year: 2006, Page(s): iv
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  • 21st Annual IEEE Conference on Computational Complexity - TOC

    Publication Year: 2006, Page(s):v - vii
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  • Preface

    Publication Year: 2006, Page(s): viii
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  • Committees

    Publication Year: 2006, Page(s): ix
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  • Reviewers

    Publication Year: 2006, Page(s): x
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  • Awards

    Publication Year: 2006, Page(s): xi
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  • Godel and Computations

    Publication Year: 2006, Page(s):3 - 5
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    Godel was born 100 years ago in this country. It is a good opportunity to commemorate this anniversary by a lecture about his influence on computational complexity. He also made contributions on computability, length of proofs, and diagonalization View full abstract»

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  • Polynomial identity testing for depth 3 circuits

    Publication Year: 2006, Page(s):9 pp. - 17
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (364 KB) | HTML iconHTML

    We study the identity testing problem for depth 3 arithmetic circuits (SigmaPiSigma circuit). We give the first deterministic polynomial time identity test for SigmaPiSigma circuits with bounded top fanin. We also show that the rank of a minimal and simple SigmaPiSigma circuit with bounded top fanin, computing zero, can be unbounded. These results answer the open questions posed by Klivans-Spielma... View full abstract»

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  • Every Linear Threshold Function has a Low-Weight Approximator

    Publication Year: 2006, Page(s):18 - 32
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (538 KB) | HTML iconHTML

    Given any linear threshold function f on n Boolean variables, we construct a linear threshold function g which disagrees with f on at most an epsiv fraction of inputs and has integer weights each of magnitude at most radicn middot 2Omacr(1/epsiv2). We show that the construction is optimal in terms of its dependence on n by proving a lower bound of Omega(radicn) on the weights required t... View full abstract»

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  • Constructions of low-degree and error-correcting /spl epsi/-biased generators

    Publication Year: 2006, Page(s):13 pp. - 45
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (478 KB) | HTML iconHTML

    In this work we give two new constructions of epsi-biased generators. Our first construction answers an open question of Dodis and Smith (2005), and our second construction significantly extends a result of Mossel et al. (2003). In particular we obtain the following results: (1) We construct a family of asymptotically good binary codes such that the codes in our family are also epsi-biased sets fo... View full abstract»

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  • How to Get More Mileage from Randomness Extractors

    Publication Year: 2006, Page(s):46 - 60
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (538 KB) | HTML iconHTML

    Let C be a class of distributions over {0, 1}n. A deterministic randomness extractor for C is a function E : {0, 1}n rarr {0, 1}m such that for any X in C the distribution E(X) is statistically close to the uniform distribution. A long line of research deals with explicit constructions of such extractors for various classes C while trying to maximize m. In this pa... View full abstract»

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  • Exposure-resilient extractors

    Publication Year: 2006, Page(s):9 pp. - 72
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (367 KB) | HTML iconHTML

    An exposure-resilient extractor is an efficient procedure that, from a random variable with imperfect min-entropy, produces randomness that passes all statistical tests including those that have bounded access to the random variable, with adaptive queries that can depend on the string being tested. More precisely, EXT : {0, 1}n times {0, 1}d rarr {0, 1}m is a (k, e... View full abstract»

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  • Making hard problems harder

    Publication Year: 2006, Page(s):15 pp. - 87
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (498 KB) | HTML iconHTML

    We consider a general approach to the hoary problem of (im)proving circuit lower bounds. We define notions of hardness condensing and hardness extraction, in analogy to the corresponding notions from the computational theory of randomness. A hardness condenser is a procedure that takes in a Boolean function as input, as well as an advice string, and outputs a Boolean function on a smaller number o... View full abstract»

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  • Distinguishing SAT from polynomial-size circuits, through black-box queries

    Publication Year: 2006, Page(s):8 pp. - 95
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (368 KB) | HTML iconHTML

    We may believe SAT does not have small Boolean circuits. But is it possible that some language with small circuits looks indistinguishable from SAT to every polynomial-time bounded adversary? We rule out this possibility. More precisely, assuming SAT does not have small circuits, we show that for every language A with small circuits, there exists a probabilistic polynomial-time algorithm that make... View full abstract»

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  • Parallel repetition of zero-knowledge proofs and the possibility of basing cryptography on NP-hardness

    Publication Year: 2006, Page(s):13 pp. - 110
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (414 KB) | HTML iconHTML

    Two long-standing open problems exist on the fringe of complexity theory and cryptography: (1) Does there exist a reduction from an NP-complete problem to a one-way function? (2) Do parallelized versions of classical constant-round zero-knowledge proofs for NP conceal every "hard" bit of the witness to the statement proved? We show that, unless the polynomial-hierarchy collapses, black-box reducti... View full abstract»

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  • Applications of the sum-product theorem in finite fields

    Publication Year: 2006, Page(s):1 pp. - 111
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (104 KB) | HTML iconHTML

    Summary form only given. About two years ago Bourgain, Katz and Tao (2004) proved the following theorem, essentially stating that in every finite field, a set which does not grow much when we add all pairs of elements, and when we multiply all pairs of elements, must be very close to a subfield. Theorem 1: (Bourgain et al., 2004) For every epsi > 0 there exists a delta > 0 such that the foll... View full abstract»

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  • Constructing Ramsey graphs from Boolean function representations

    Publication Year: 2006, Page(s):14 pp. - 128
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (830 KB) | HTML iconHTML

    Explicit construction of Ramsey graphs or graphs with no large clique or independent set has remained a challenging open problem for a long time. While Erdos' probabilistic argument shows the existence of graphs on 2n vertices with no clique or independent set of size 2n, the best explicit constructions achieve a far weaker bound. Constructing Ramsey graphs is closely related to polynom... View full abstract»

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  • A generic time hierarchy for semantic models with one bit of advice

    Publication Year: 2006, Page(s):14 pp. - 144
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (516 KB) | HTML iconHTML

    We show that for any reasonable semantic model of computation and for any positive integer a and rationals 1 < c < d, there exists a language computable in time nd with a bits of advice but not in time nc with a bits of advice. A semantic model is one for which there exists a computable enumeration that contains all machines in the model but may also contain others. We ... View full abstract»

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  • Hardness of the covering radius problem on lattices

    Publication Year: 2006, Page(s):14 pp. - 158
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (586 KB) | HTML iconHTML

    We provide the first hardness result for the covering radius problem on lattices (CRP). Namely, we show that for any large enough p les infin there exists a constant cp > 1 such that CRP in the lscrp norm is Pi2-hard to approximate to within any constant less than cp. In particular, for the case p = infin, we obtain the constant Cinfin = 1.... View full abstract»

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  • A 3-query non-adaptive PCP with perfect completeness

    Publication Year: 2006, Page(s):11 pp. - 169
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (627 KB) | HTML iconHTML

    We study a very basic open problem regarding the PCP characterization of NP, namely, the power of PCPs with 3 non-adaptive queries and perfect completeness. The lowest soundness known till now for such a PCP is 6/8 + epsi given by a construction of Hastad (1997). However, Zwick (1998) shows that a 3-query non-adaptive PCP with perfect completeness cannot achieve soundness below 5/8. In this paper,... View full abstract»

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  • New Lower Bounds for Vertex Cover in the Lovasz-Schrijver Hierarchy

    Publication Year: 2006, Page(s):170 - 182
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (377 KB) | HTML iconHTML

    Lovdsz and Schrijver (1991) defined three progressively stronger procedures LS0, LS and LS+, for systematically tightening linear relaxations over many rounds. All three procedures yield the integral hull after at most n rounds. On the other hand, constant rounds of LS+ can derive the relaxations behind many famous approximation algorithms such as those for MAX-CUT... View full abstract»

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  • FO[<]-uniformity

    Publication Year: 2006, Page(s):7 pp. - 189
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (301 KB) | HTML iconHTML

    Uniformity notions more restrictive than the usual FO[<, +, *]-uniformity = FO[<, Bit]-uniformity are introduced. It is shown that the general framework exhibited by Barrington et al. still holds if the fan-in of the gates in the corresponding circuits is considered View full abstract»

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  • Circuit lower bounds via Ehrenfeucht-Fraisse games

    Publication Year: 2006, Page(s):12 pp. - 201
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (488 KB) | HTML iconHTML

    In this paper we prove that the class of functions expressible by first order formulas with only two variables coincides with the class of functions computable by AC0 circuits with a linear number of gates. We then investigate the feasibility of using Ehrenfeucht-Fraisse games to prove lower bounds for that class of circuits, as well as for general AC0 circuits View full abstract»

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