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2009 24th Annual IEEE Conference on Computational Complexity

15-18 July 2009

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  • [Front cover]

    Publication Year: 2009, Page(s): C1
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  • [Title page i]

    Publication Year: 2009, Page(s): i
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  • [Title page iii]

    Publication Year: 2009, Page(s): iii
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  • [Copyright notice]

    Publication Year: 2009, Page(s): iv
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  • Table of contents

    Publication Year: 2009, Page(s):v - vii
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  • Conference Information

    Publication Year: 2009, Page(s):viii - xi
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  • Poly-logarithmic Independence Fools AC^0 Circuits

    Publication Year: 2009, Page(s):3 - 8
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (291 KB) | HTML iconHTML

    We prove that poly-sized AC0 circuits cannot distinguish a poly-logarithmically independent distribution from the uniform one. This settles the 1990 conjecture by Linial and Nisan [LN90]. The only prior progress on the problem was by Bazzi [Baz07], who showed that O(log2n)-independent distributions fool poly-size DNF formulas. Razborov [Raz08] has later given a much simpler p... View full abstract»

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  • k-Subgraph Isomorphism on AC_0 Circuits

    Publication Year: 2009, Page(s):9 - 18
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (412 KB) | HTML iconHTML

    Recently, Rossman [STOC '08] established a lower bound of omega(nk/4) on the size of constant-depth circuits for the k-clique function on n-vertex graphs, which is the first lower bound that does not depend on the depth of circuits in the exponent of n. He showed, in fact, a stronger statement: Suppose fn : {0, 1}(n/2) rarr {0,1} is a sequence of functions computed... View full abstract»

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  • Fixed-Polynomial Size Circuit Bounds

    Publication Year: 2009, Page(s):19 - 26
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (302 KB) | HTML iconHTML

    In 1982, Kannan showed that SigmaP 2 does not have nk-sized circuits for any k. Do smaller classes also admit such circuit lower bounds? Despite several improvements of Kannan's result, we still cannot prove that PNP does not have linear size circuits. Work of Aaronson and Wigderson provides strong evidence - the "algebrization'' barrier - that current t... View full abstract»

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  • A New Characterization of ACC^0 and Probabilistic CC^0

    Publication Year: 2009, Page(s):27 - 34
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (335 KB) | HTML iconHTML

    Barrington, Straubing and Therien (1990) conjectured that the Boolean AND function can not be computed by polynomial size constant depth circuits built from modular counting gates, i.e., by CC0 circuits. In this work we show that the AND function can be computed by uniform probabilistic CC0 circuits that use only O(log n) random bits. This may be viewed as evidence contrary t... View full abstract»

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  • A Superpolynomial Lower Bound on the Size of Uniform Non-constant-depth Threshold Circuits for the Permanent

    Publication Year: 2009, Page(s):35 - 40
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (257 KB) | HTML iconHTML

    We show that the permanent cannot be computed by DLOGTIME-uniform threshold or arithmetic circuits of depth o(log log n) and polynomial size. View full abstract»

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  • The Proof Complexity of Polynomial Identities

    Publication Year: 2009, Page(s):41 - 51
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (373 KB) | HTML iconHTML

    Devising an efficient deterministic - or even a non-deterministic sub-exponential time - algorithm for testing polynomial identities is a fundamental problem in algebraic complexity and complexity at large. Motivated by this problem, as well as by results from proof complexity, we investigate the complexity of proving polynomial identities. To this end, we study a class of equational proof systems... View full abstract»

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  • Locally Testable Codes Require Redundant Testers

    Publication Year: 2009, Page(s):52 - 61
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (328 KB) | HTML iconHTML

    Locally testable codes (LTCs) are error- correcting codes for which membership, in the code, of a given word can be tested by examining it in very few locations. Most known constructions of locally testable codes are linear codes, and give error-correcting codes whose duals have (superlinearly) many small weight codewords. Examining this feature appears to be one of the promising approaches to pro... View full abstract»

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  • Every Permutation CSP of arity 3 is Approximation Resistant

    Publication Year: 2009, Page(s):62 - 73
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (415 KB) | HTML iconHTML

    A permutation constraint satisfaction problem (permCSP) of arity k is specified by a subset LambdasubeSk of permutations on {1,2,...,k}. An instance of such a permCSP consists of a set of variables V and a collection of constraints each of which is an ordered k-tuple of V. The objective is to find a global ordering sigma of the variables that maximizes the number of constraint tuples wh... View full abstract»

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  • Inapproximability of Vertex Cover and Independent Set in Bounded Degree Graphs

    Publication Year: 2009, Page(s):74 - 80
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (313 KB) | HTML iconHTML

    We study the inapproximability of Vertex Cover and Independent Set on degree d graphs. We prove that: (1) Vertex Cover is Unique Games-hard to approximate to within a factor 2 - (2 + od(1)) log log d/log d. This exactly matches the algorithmic result of Halperin up to the od(1) term. (2) Independent Set is Unique Games-hard to approximate to within a factor O(d/log2 View full abstract»

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  • Are PCPs Inherent in Efficient Arguments?

    Publication Year: 2009, Page(s):81 - 92
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (353 KB) | HTML iconHTML

    Starting with Kilian (STOC '92), several works have shown how to use probabilistically checkable proofs (PCPs) and cryptographic primitives such as collision-resistant hashing to construct very efficient argument systems (a.k.a. computationally sound proofs), for example with polylogarithmic communication complexity. Ishai et al. (CCC `07) raised the question of whether PCPs are inherent in effici... View full abstract»

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  • Extractors for Low-Weight Affine Sources

    Publication Year: 2009, Page(s):95 - 101
    Cited by:  Papers (14)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (316 KB) | HTML iconHTML

    We give polynomial time computable extractors for low-weight affine sources. A distribution is affine if it samples a random points from some unknown low dimensional subspace of F2 n. A distribution is low weight affine if the corresponding linear space has a basis of low-weight vectors. Low-weight affine sources are thus a generalization of the well studied models of bit-fix... View full abstract»

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  • Extractors for Varieties

    Publication Year: 2009, Page(s):102 - 113
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (361 KB) | HTML iconHTML

    We study the task of randomness extraction from sources which are distributed uniformly on an unknown algebraic variety. In other words, we are interested in constructing a function (an extractor) whose output is close to uniform even if the input is drawn uniformly from the set of solutions of an unknown system of low degree polynomials. This problem generalizes the problem of extraction from aff... View full abstract»

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  • Weak Derandomization of Weak Algorithms: Explicit Versions of Yao's Lemma

    Publication Year: 2009, Page(s):114 - 125
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (393 KB) | HTML iconHTML

    A simple averaging argument shows that given a randomized algorithm A and a function f such that for every input x, Pr[A(x) = f(x)] ges 1-p (where the probability is over the coin tosses of A), there exists a nonuniform deterministic algorithm B "of roughly the same complexity'' such that Pr[B(x) = f(x)] ges 1-p (where the probability is over a uniformly chosen input x). This implication is often ... View full abstract»

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  • Regularity, Boosting, and Efficiently Simulating Every High-Entropy Distribution

    Publication Year: 2009, Page(s):126 - 136
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (391 KB) | HTML iconHTML

    We show that every bounded function g: {0,1}n rarr [0,1] admits an efficiently computable "simulator" function h: {0,1}n rarr [0,1] such that every fixed polynomial size circuit has approximately the same correlation with g as with h. If g describes (up to scaling) a high min-entropy distribution D, then h can be used to efficiently sample a distribution D' of the same min-en... View full abstract»

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  • An Almost Optimal Rank Bound for Depth-3 Identities

    Publication Year: 2009, Page(s):137 - 148
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (382 KB) | HTML iconHTML

    We show that the rank of a depth-3 circuit (over any field) that is simple, minimal and zero is at most O(k3 log d). The previous best rank bound known was 2O(k2)(log d)k-2 by Dvir and Shpilka (STOC 2005). This almost resolves the rank question first posed by Dvir and Shpilka (as we also provide a simple and minimal identity of rank Omega(k log d)). Our rank bound ... View full abstract»

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  • Lipschitz Continuous Ordinary Differential Equations are Polynomial-Space Complete

    Publication Year: 2009, Page(s):149 - 160
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (323 KB) | HTML iconHTML

    In answer to Ko's question raised in 1983, we show that an initial value problem given by a polynomial-time computable, Lipschitz continuous function can have a polynomial-space complete solution. The key insight is simple: the Lipschitz condition means that the feedback in the differential equation is weak. We define a class of polynomial-space computation tableaux with equally restricted feedbac... View full abstract»

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  • Improved Approximation of Linear Threshold Functions

    Publication Year: 2009, Page(s):161 - 172
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (424 KB) | HTML iconHTML

    We prove two main results on how arbitrary linear threshold functions f(x) = sign(w ldr x - thetas) over the n-dimensional Boolean hypercube can be approximated by simple threshold functions. Our first result shows that every n-variable threshold function f is isin-close to a threshold function depending only on Inf(f)2 ldr poly (1/isin) many variables, where Inf(f) denotes the total in... View full abstract»

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  • On the Complexity of Boolean Functions in Different Characteristics

    Publication Year: 2009, Page(s):173 - 183
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (392 KB) | HTML iconHTML

    Every Boolean function on n variables can be expressed as a unique multivariate polynomial modulo p for every prime p. In this work, we study how the degree of a function in one characteristic affects its complexity in other characteristics. We establish the following general principle: functions with low degree modulo p must have high complexity in every other characteristic q. More precisely, we... View full abstract»

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  • The Complexity of the Annihilating Polynomial

    Publication Year: 2009, Page(s):184 - 193
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (374 KB) | HTML iconHTML

    Let F be a field and f1,..., fk in F[x1, ..., xn] be a set of k polynomials of degree d in n variables over the field F. These polynomials are said to be algebraically dependent if there exists a nonzero k-variate polynomial A(t1, ..., tk) in F[t1, ..., tk] such that A(f1, ..., fk) = 0. A ... View full abstract»

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