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Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07)

13-16 June 2007

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  • Twenty-Second Annual IEEE Conference on Computational Complexity-Title

    Publication Year: 2007, Page(s):i - iii
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  • Twenty-Second Annual IEEE Conference on Computational Complexity-Copyright

    Publication Year: 2007, Page(s): iv
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  • Twenty-Second Annual IEEE Conference on Computational Complexity - TOC

    Publication Year: 2007, Page(s):v - vii
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  • Preface

    Publication Year: 2007, Page(s): viii
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  • Committees

    Publication Year: 2007, Page(s): ix
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  • Ronald V. Book Prize for Best Student Paper Award

    Publication Year: 2007, Page(s): x
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  • Awards [2 awards]

    Publication Year: 2007, Page(s): x
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  • Reviewers

    Publication Year: 2007, Page(s): xi
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  • On Derandomizing Probabilistic Sublinear-Time Algorithms

    Publication Year: 2007, Page(s):1 - 9
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (190 KB) | HTML iconHTML

    There exists a positive constant alpha < 1 such that for any function T(n) les n alpha and for any problem L isin BPTIME(T(n)), there exists a deterministic algorithm running in poly(T(n)) time which decides L, except for at most a 2-Omega (T(n) log T(n)) fraction of inputs of length ... View full abstract»

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  • The Communication Complexity of Correlation

    Publication Year: 2007, Page(s):10 - 23
    Cited by:  Papers (17)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (259 KB) | HTML iconHTML

    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 the knowledge of D. There are two settings based on how the distribution D provided to Alice is chosen. ... View full abstract»

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  • On Computation and Communication with Small Bias

    Publication Year: 2007, Page(s):24 - 32
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (186 KB) | HTML iconHTML

    We present two results for computational models that allow error probabilities close to 1/2. First, most computational complexity classes have an analogous class in communication complexity. The class PP in fact has two, a version with weakly restricted bias called PPcc, and a version with unrestricted bias called UPPcc. Ever since their introduction by Babai, Frankl, and Sim... View full abstract»

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  • Lower Bounds for Multi-Player Pointer Jumping

    Publication Year: 2007, Page(s):33 - 45
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (239 KB) | HTML iconHTML

    We consider the k-layer pointer jumping problem in the one-way multi-party number-on-the-forehead communication model. Sufficiently strong lower bounds for the problem would have major consequences in circuit complexity. We take an information complexity approach to this problem and obtain three lower bounds that improve upon earlier work. For myopic protocols (where players may see only one layer... View full abstract»

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  • Low-Depth Witnesses are Easy to Find

    Publication Year: 2007, Page(s):46 - 51
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (138 KB) | HTML iconHTML

    Antunes, Fortnow, van Melkebeek and Vinodchandran captured the notion of non-random information by computational depth, the difference between the polynomial-time- bounded Kolmogorov complexity and traditional Kolmogorov complexity. We show unconditionally how to probabilistically find satisfying assignments for formulas that have at least one assignment of logarithmic depth. The converse holds un... View full abstract»

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  • Bounded Queries and the NP Machine Hypothesis

    Publication Year: 2007, Page(s):52 - 59
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (158 KB) | HTML iconHTML

    The NP machine hypothesis posits the existence of an in ge 0 and a nondeterministic polynomial-time Turing machine M which accepts the language 0 but for which no deterministic Turing machine running in 2^n time can output an accepting path infinitely often. This paper shows two applications of the NP machine hypothesis in bounded query complexity. First, if the NP machine hypothesis holds, then P... View full abstract»

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  • On C-Degrees, H-Degrees and T-Degrees

    Publication Year: 2007, Page(s):60 - 69
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (222 KB) | HTML iconHTML

    Following a line of research that aims at relating the computation power and the initial segment complexity of a set, the work presented here investigates into the relations between Turing reducibility, defined in terms of computation power, and C-reducibility and H-reducibility, defined in terms of the complexity of initial segments. The global structures of all C-degrees and of all H-degrees are... View full abstract»

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  • Time-Space Tradeoffs for Counting NP Solutions Modulo Integers

    Publication Year: 2007, Page(s):70 - 82
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (213 KB) | HTML iconHTML

    We prove the first time-space tradeoffs for counting the number of solutions to an NP problem modulo small integers, and also improve upon the known time-space tradeoffs for SAT. Let m be a positive integer, and define MOD_m- SAT to be the problem of determining if a given Boolean formula has exactly km satisfying assignments, for some integer k. We prove that for all primes p, except for possibly... View full abstract»

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  • Halfspace Matrices

    Publication Year: 2007, Page(s):83 - 95
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (271 KB) | HTML iconHTML

    A halfspace matrix is a Boolean matrix A with rows indexed by linear threshold functions f , columns indexed by inputs x isin {-1,1}n, and the entries given by Af ,x = f (x). We demonstrate the potential of halfspace matrices as tools to answer nontrivial open questions. (1) (Communication complexity) We exhibit a Boolean function f with discrepancy Omega(1/n... View full abstract»

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  • Unbalanced Expanders and Randomness Extractors from Parvaresh-Vardy Codes

    Publication Year: 2007, Page(s):96 - 108
    Cited by:  Papers (20)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (244 KB) | HTML iconHTML

    We give an improved explicit construction of highly unbalanced bipartite expander graphs with expansion arbitrarily close to the degree (which is polylogarithmic in the number of vertices). Both the degree and the number of right-hand vertices are polynomially close to optimal, whereas the previous constructions of Ta-Shma, Umans, and Zuckerman (STOC "01) required at least one of these to be quasi... View full abstract»

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  • Perfect Parallel Repetition Theorem for Quantum XOR Proof Systems

    Publication Year: 2007, Page(s):109 - 114
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (161 KB) | HTML iconHTML

    We consider a class of two-prover interactive proof systems where each prover returns a single bit to the verifier and the verifier's verdict is a function of the XOR of the two bits received. We show that, when the provers are allowed to coordinate their behavior using a shared entangled quantum state, a perfect parallel repetition theorem holds in the following sense. The prover's optimal succes... View full abstract»

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  • Quantum versus Classical Proofs and Advice

    Publication Year: 2007, Page(s):115 - 128
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (287 KB) | HTML iconHTML

    This paper studies whether quantum proofs are more powerful than classical proofs, or in complexity terms, whether QMA = QCMA. We prove three results about this question. First, we give a "quantum oracle separation" between QMA and QCM A. More concretely, we show that any quantum algorithm needs Omega (radic2n-m+1) queries to find an n-qubit "marked state" Psi rang, even if g... View full abstract»

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  • Quantum t-designs: t-wise Independence in the Quantum World

    Publication Year: 2007, Page(s):129 - 140
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (221 KB) | HTML iconHTML

    A t-design for quantum states is a finite set of quantum states with the property of simulating the Haar-measure on quantum states w.r.t. any test that uses at most t copies of a state. We give efficient constructions for approximate quantum t-designs for arbitrary t. We then show that an approximate 4-design provides a derandomization of the statedistinction problem considered by Sen (quant-ph/05... View full abstract»

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  • Norms, XOR Lemmas, and Lower Bounds for GF(2) Polynomials and Multiparty Protocols

    Publication Year: 2007, Page(s):141 - 154
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (302 KB) | HTML iconHTML

    This paper presents a unified and simple treatment of basic questions concerning two computational models: multiparty communication complexity and GF(2) polynomials. The key is the use of (known) norms on Boolean functions, which capture their approximability in each of these models. The main contributions are new XOR lemmas. We show that if a Boolean function has correlation at most epsi les 1/2 ... View full abstract»

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  • On Approximate Majority and Probabilistic Time

    Publication Year: 2007, Page(s):155 - 168
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (293 KB) | HTML iconHTML

    We prove new results on the circuit complexity of approximate majority, which is the problem of computing majority of a given bit string whose fraction of 1's is bounded away from 1/2 (by a constant). We then apply these results to obtain new relationships between probabilistic time, BPTime (t), and alternating time, SigmaO(1)Time (t). View full abstract»

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  • An Exponential Lower Bound on the Size of Constant-Depth Threshold Circuits with Small Energy Complexity

    Publication Year: 2007, Page(s):169 - 178
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (238 KB) | HTML iconHTML

    A complexity measure for threshold circuits, called the energy complexity, has been proposed to measure an amount of energy consumed during computation in the brain. Biological neurons need more energy to transmit a "spike" than not to transmit one, and hence the energy complexity of a threshold circuit is defined as the number of gates in the circuit that output "1" during computation. Since the ... View full abstract»

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  • Understanding Parallel Repetition Requires Understanding Foams

    Publication Year: 2007, Page(s):179 - 192
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (582 KB) | HTML iconHTML

    Motivated by the study of parallel repetition and also by the unique games conjecture, we investigate the value of the "odd cycle games" under parallel repetition. Using tools from discrete harmonic analysis, we show that after d rounds on the cycle of length m, the value of the game is at most 1-(1/m)ldrOmega macr(radicd) (for dlesm2, say). This beats the natural barrier of 1-Theta(1/m... View full abstract»

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