2326 June 2008
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[Front cover]
Publication Year: 2008, Page(s): C1 PDF (184 KB) 
[Title page i]
Publication Year: 2008, Page(s): i PDF (58 KB) 
[Title page iii]
Publication Year: 2008, Page(s): iii PDF (109 KB) 
[Copyright notice]
Publication Year: 2008, Page(s): iv PDF (113 KB) 
Table of contents
Publication Year: 2008, Page(s):v  viii PDF (231 KB) 

Committees
Publication Year: 2008, Page(s): x PDF (112 KB) 
listreviewer
Publication Year: 2008, Page(s): xi PDF (101 KB) 
Awards
Publication Year: 2008, Page(s): xii PDF (91 KB) 
NPHard Sets Are Exponentially Dense Unless coNP C NP/poly
Publication Year: 2008, Page(s):1  7
Cited by: Papers (5)We show that hard sets S for NP must have exponential density, i.e. S<sub>=n</sub> ges 2n<sup>epsi</sup> for some isin > 0 and infinitely many n, unless coNP sube NP/poly and the polynomialtime hierarchy collapses. This result holds for Turing reductions that make n<sup>1isin</sup> queries. In addition we study the instance complexity o/NP hard probl... View full abstract»

Approximation of Natural W[P]Complete Minimisation Problems Is Hard
Publication Year: 2008, Page(s):8  18
Cited by: Papers (5)We prove that the weighted monotone circuit satisfiability problem has no fixedparameter 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 fixedparameter tractable 2approximation algorithm unless every prob... View full abstract»

Hardness Amplification within NP against Deterministic Algorithms
Publication Year: 2008, Page(s):19  30
Cited by: Papers (1)We study the averagecase 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»

Amplifying Lower Bounds by Means of SelfReducibility
Publication Year: 2008, Page(s):31  40
Cited by: Papers (4)We observe that many important computational problems in NC1share a simple selfreducibility property. We then show that, for any problem A having this selfreducibility property, A has polynomial size TC0circuits if and only if it has TC0circuits of size n1+isinfor every isin>0 (counting the number of wires in a circuit as the size of the circuit). A... View full abstract»

Amplifying ZPP^SAT[1] and the Two Queries Problem
Publication Year: 2008, Page(s):41  52This 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, ZPP<sup>SAT[1]</sup> = ZPP<sup>SAT[2]</sup> rArr ZPP<sup>SAT[1]</sup> = 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). Th... View full abstract»

Learning Complexity vs. Communication Complexity
Publication Year: 2008, Page(s):53  63
Cited by: Papers (2)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»

Communication Complexity under Product and Nonproduct Distributions
Publication Year: 2008, Page(s):64  70
Cited by: Papers (1)We solve an open problem in communication complexity posed by Kushilevitz and Nisan (1997). Let R<sub>epsiv</sub>(f) and D<sup>mu</sup> <sub>epsiv</sub>(f) denote the randomized and mudistributional communication complexities off, respectively (e a small constant). Yao's wellknown minimax principle states that R<sub>epsiv</sub>(f) = max<sub>m... View full abstract»

A Direct Product Theorem for Discrepancy
Publication Year: 2008, Page(s):71  80
Cited by: Papers (13)Discrepancy is a versatile bound in communication complexity which can be used to show lower bounds in randomized, quantum, and even weaklyunbounded 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»

Disjointness Is Hard in the Multiparty NumberontheForehead Model
Publication Year: 2008, Page(s):81  91
Cited by: Papers (3)We show that disjointness requires randomized communication Omega(n<sup>1/(k+1)</sup>/2<sup>2</sup> <sup>k</sup>) in the general kparty numberontheforehead model of complexity. The previous best lower bound was Omega (log n/k1). By results of Beame, Pitassi, and Segerlind, this implies 2<sup>n</sup> <sup>Omega(1)</sup> lower bounds o... View full abstract»

Constant Width Planar Branching Programs Characterize ACC^0 in Quasipolynomial Size
Publication Year: 2008, Page(s):92  99We 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 Pi<sub>2</sub> o CC<sup>0</sup> o AC<sup>0</sup> circuit in polynomial size. In the quasipolynomial size setting we obtain a characterization of ACC<sup>0</sup> by const... View full abstract»

On the Relative Efficiency of ResolutionLike Proofs and Ordered Binary Decision Diagram Proofs
Publication Year: 2008, Page(s):100  111
Cited by: Papers (2)We show that treelike OBDD proofs of unsatisfiability require an exponential increase (s rarr 2<sup>s</sup> <sup>Omega(1)</sup>) in proof size to simulate unrestricted resolution, and that unrestricted OBDD proofs of unsatisfiability require an almostexponential increase (s rarr 2<sup>2(log</sup> <sup>s)</sup> <sup>Omega(1)</sup>) in pr... View full abstract»

Approximate InclusionExclusion for Arbitrary Symmetric Functions
Publication Year: 2008, Page(s):112  123
Cited by: Papers (2)Let A_1,..., A_n be events in a probability space. The approximate inclusionexclusion 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 LinialNisan 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»

The Sum of d SmallBias Generators Fools Polynomials of Degree d
Publication Year: 2008, Page(s):124  127
Cited by: Papers (6)We prove that the sum of d smallbias generators L : F<sup>s</sup> rarr F<sup>n</sup> fools degreed polynomials in n variables over a prime field F, for any fixed degree d and field F, including F = F<sub>2</sub> = {0,1}. Our result improves on both the work by Bogdanov and Viola (FOCS '07) and the beautiful followup by Lovett (STOC '08). The first relies on a... View full abstract»

Lower Bounds and Separations for Constant Depth Multilinear Circuits
Publication Year: 2008, Page(s):128  139
Cited by: Papers (4)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 superpolynomial separation between the size of productdepth d and productdepth d+1 multilinear circuits (where d is constant). That i... View full abstract»

Noisy Interpolating Sets for Low Degree Polynomials
Publication Year: 2008, Page(s):140  148A noisy interpolating set (NIS) for degree d polynomials is a set S sube F<sup>n</sup>, where F is a finite field, such that any degree d polynomial q isin F[x<sub>1</sub>,..., x<sub>n</sub>] 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 pri... View full abstract»

Constraint Logic: A Uniform Framework for Modeling Computation as Games
Publication Year: 2008, Page(s):149  162
Cited by: Papers (5)We introduce a simple game family, called constraint logic, where players reverse edges in a directed graph while satisfying vertex inflow constraints. This game family can be interpreted in many different gametheoretic settings, ranging from zeroplayer 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»