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2008 23rd Annual IEEE Conference on Computational Complexity

23-26 June 2008

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Displaying Results 1 - 25 of 43
  • [Front cover]

    Publication Year: 2008, Page(s): C1
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  • [Title page i]

    Publication Year: 2008, Page(s): i
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  • [Title page iii]

    Publication Year: 2008, Page(s): iii
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  • [Copyright notice]

    Publication Year: 2008, Page(s): iv
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  • Table of contents

    Publication Year: 2008, Page(s):v - viii
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  • Preface

    Publication Year: 2008, Page(s): ix
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  • Committees

    Publication Year: 2008, Page(s): x
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  • list-reviewer

    Publication Year: 2008
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  • Awards

    Publication Year: 2008, Page(s): xii
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  • NP-Hard Sets Are Exponentially Dense Unless coNP C NP/poly

    Publication Year: 2008, Page(s):1 - 7
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (366 KB) | HTML iconHTML

    We show that hard sets S for NP must have exponential density, i.e. |S=n| ges 2nepsi for some isin > 0 and infinitely many n, unless coNP sube NP/poly and the polynomial-time hierarchy collapses. This result holds for Turing reductions that make n1-isin queries. In addition we study the instance complexity o/NP- hard problems and show that hard sets also have an... View full abstract»

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  • Approximation of Natural W[P]-Complete Minimisation Problems Is Hard

    Publication Year: 2008, Page(s):8 - 18
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (415 KB) | HTML iconHTML

    We prove that the weighted monotone circuit satisfiability problem has no fixed-parameter tractable approximation algorithm with constant or polylogarithmic approximation ratio unless FPT = W[P]. Our result answers a question of Alekhnovich and Razborov, who proved that the weighted monotone circuit satisfiability problem has no fixed-parameter tractable 2-approximation algorithm unless every prob... View full abstract»

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  • Hardness Amplification within NP against Deterministic Algorithms

    Publication Year: 2008, Page(s):19 - 30
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (458 KB) | HTML iconHTML

    We study the average-case hardness of the class NP against deterministic polynomial time algorithms. We prove that there exists some constant mu Gt 0 such that if there is some language in NP for which no deterministic polynomial time algorithm can decide L correctly on a 1 - (log n)-mu fraction of inputs of length n, then there is a language L' in NP for which no deterministic polynomial time alg... View full abstract»

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  • Amplifying Lower Bounds by Means of Self-Reducibility

    Publication Year: 2008, Page(s):31 - 40
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (404 KB) | HTML iconHTML

    We observe that many important computational problems in NC1 share a simple self-reducibility property. We then show that, for any problem A having this self-reducibility property, A has polynomial size TC0 circuits if and only if it has TC0 circuits of size n1+isin for every isin>0 (counting the number of wires in a circuit as the size of the circuit... View full abstract»

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  • Amplifying ZPP^SAT[1] and the Two Queries Problem

    Publication Year: 2008, Page(s):41 - 52
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (415 KB) | HTML iconHTML

    This paper shows a complete upward collapse in the Polynomial Hierarchy (PH) if for ZPP, two queries to a SAT oracle is equivalent to one query. That is, ZPPSAT[1] = ZPPSAT||[2] rArr ZPPSAT[1] = PH. These ZPP machines are required to succeed with probability at least 1/2 + 1/p(n) on inputs of length n for some polynomial p(n). This result builds upon recent work by... View full abstract»

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  • Learning Complexity vs. Communication Complexity

    Publication Year: 2008, Page(s):53 - 63
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (381 KB) | HTML iconHTML

    This paper has two main focal points. We first consider an important class of machine learning algorithms - large margin classifiers, such as support vector machines. The notion of margin complexity quantifies the extent to which a given class of functions can be learned by large margin classifiers. We prove that up to a small multiplicative constant, margin complexity is equal to the inverse of d... View full abstract»

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  • Communication Complexity under Product and Nonproduct Distributions

    Publication Year: 2008, Page(s):64 - 70
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (363 KB) | HTML iconHTML

    We solve an open problem in communication complexity posed by Kushilevitz and Nisan (1997). Let Repsiv(f) and Dmu epsiv(f) denote the randomized and mu-distributional communication complexities off, respectively (e a small constant). Yao's well-known minimax principle states that Repsiv(f) = maxmu{Dmu epsiv(f)}. Kushilevi... View full abstract»

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  • A Direct Product Theorem for Discrepancy

    Publication Year: 2008, Page(s):71 - 80
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (394 KB) | HTML iconHTML

    Discrepancy is a versatile bound in communication complexity which can be used to show lower bounds in randomized, quantum, and even weakly-unbounded error models of communication. We show an optimal product theorem for discrepancy, namely that for any two Boolean functions f, g, disc(f odot g)=thetas(disc(f) disc(g)). As a consequence we obtain a strong direct product theorem for distributional c... View full abstract»

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  • Disjointness Is Hard in the Multi-party Number-on-the-Forehead Model

    Publication Year: 2008, Page(s):81 - 91
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (418 KB) | HTML iconHTML

    We show that disjointness requires randomized communication Omega(n1/(k+1)/22 k) in the general k-party number-on-the-forehead model of complexity. The previous best lower bound was Omega (log n/k-1). By results of Beame, Pitassi, and Segerlind, this implies 2n Omega(1) lower bounds on the size of tree-like Lovasz-Schrijver proof systems neede... View full abstract»

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  • Constant Width Planar Branching Programs Characterize ACC^0 in Quasipolynomial Size

    Publication Year: 2008, Page(s):92 - 99
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (348 KB) | HTML iconHTML

    We revisit the computational power of constant width polynomial size planar nondeterministic branching programs. We show that they are capable of computing any function computed by a Pi2 o CC0 o AC0 circuit in polynomial size. In the quasipolynomial size setting we obtain a characterization of ACC0 by constant width planar non-deterministic branching pro... View full abstract»

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  • On the Relative Efficiency of Resolution-Like Proofs and Ordered Binary Decision Diagram Proofs

    Publication Year: 2008, Page(s):100 - 111
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (449 KB) | HTML iconHTML

    We show that tree-like OBDD proofs of unsatisfiability require an exponential increase (s rarr 2s Omega(1)) in proof size to simulate unrestricted resolution, and that unrestricted OBDD proofs of unsatisfiability require an almost-exponential increase (s rarr 22(log s) Omega(1)) in proof size to simulate Res (O(log n)). The "OBDD proof system"... View full abstract»

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  • Approximate Inclusion-Exclusion for Arbitrary Symmetric Functions

    Publication Year: 2008, Page(s):112 - 123
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (440 KB) | HTML iconHTML

    Let A_1,..., A_n be events in a probability space. The approximate inclusion-exclusion problem, due to Linial and Nisan (1990), is to estimate Prob [A_1 OR ... OR A_n] given Prob [AND_{i in S} A_i] for |S|{0,1} is a given symmetric function. (In the Linial-Nisan problem, f=OR.). We solve this general problem for every f and k, giving an algorithm that runs in polynomial time and achieves an approx... View full abstract»

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  • The Sum of d Small-Bias Generators Fools Polynomials of Degree d

    Publication Year: 2008, Page(s):124 - 127
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (333 KB) | HTML iconHTML

    We prove that the sum of d small-bias generators L : Fs rarr Fn fools degree-d polynomials in n variables over a prime field F, for any fixed degree d and field F, including F = F2 = {0,1}. Our result improves on both the work by Bogdanov and Viola (FOCS '07) and the beautiful follow-up by Lovett (STOC '08). The first relies on a conjecture that turned out to be tr... View full abstract»

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  • Lower Bounds and Separations for Constant Depth Multilinear Circuits

    Publication Year: 2008, Page(s):128 - 139
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (421 KB) | HTML iconHTML

    We prove an exponential lower bound for the size of constant depth multilinear arithmetic circuits computing either the determinant or the permanent (a circuit is called multilinear, if the polynomial computed by each of its gates is multilinear). We also prove a super-polynomial separation between the size of product-depth d and product-depth d+1 multilinear circuits (where d is constant). That i... View full abstract»

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  • Noisy Interpolating Sets for Low Degree Polynomials

    Publication Year: 2008, Page(s):140 - 148
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (368 KB) | HTML iconHTML

    A noisy interpolating set (NIS) for degree d polynomials is a set S sube Fn, where F is a finite field, such that any degree d polynomial q isin F[x1,..., xn] can be efficiently interpolated from its values on S, even if an adversary corrupts a constant fraction of the values. In this paper we construct explicit NIS for every prime field Fp and any degre... View full abstract»

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  • Constraint Logic: A Uniform Framework for Modeling Computation as Games

    Publication Year: 2008, Page(s):149 - 162
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2809 KB) | HTML iconHTML

    We introduce a simple game family, called constraint logic, where players reverse edges in a directed graph while satisfying vertex in-flow constraints. This game family can be interpreted in many different game-theoretic settings, ranging from zero-player automata to a more economic setting of team multiplayer games with hidden information. Each setting gives rise to a model of computation that w... View full abstract»

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