20th Annual IEEE Conference on Computational Complexity (CCC'05)

11-15 June 2005

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  • Twentieth Annual IEEE Conference on Computational Complexity - Cover

    Publication Year: 2005, Page(s): c1
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  • Twentieth Annual IEEE Conference on Computational Complexity - Title Page

    Publication Year: 2005, Page(s):i - iii
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  • Twentieth Annual IEEE Conference on Computational Complexity - Copyright Page

    Publication Year: 2005, Page(s): iv
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  • Twentieth Annual IEEE Conference on Computational Complexity - Table of contents

    Publication Year: 2005, Page(s):v - vii
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  • Preface

    Publication Year: 2005, Page(s): viii
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  • Committees

    Publication Year: 2005, Page(s): ix
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  • Awards

    Publication Year: 2005, Page(s): x
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  • On the ring isomorphism & automorphism problems

    Publication Year: 2005, Page(s):2 - 12
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (215 KB) | HTML iconHTML

    We study the complexity of the isomorphism and automorphism problems for finite rings with unity. We show that both integer factorization and graph isomorphism reduce to the problem of counting automorphisms of rings. The problem is shown to be in the complexity class AM /spl cap/ coAM and hence is not NP-complete unless the polynomial hierarchy collapses. Integer factorization also reduces to the... View full abstract»

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  • Bounded color multiplicity graph isomorphism is in the #L hierarchy

    Publication Year: 2005, Page(s):13 - 27
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (285 KB) | HTML iconHTML

    In this paper we study the complexity of bounded color multiplicity graph isomorphism BCGI/sub b/: the input is a pair of vertex-colored graphs such that the number of vertices of a given color in an input graph is bounded by b. We show that BCGI/sub b/ is in the #L hierarchy (more precisely, the Mod/sub k/L hierarchy for some constant k depending on b). Combined with the fact that bounded color m... View full abstract»

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  • The complexity of the inertia and some closure properties of GapL

    Publication Year: 2005, Page(s):28 - 37
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (174 KB) | HTML iconHTML

    The inertia of an n /spl times/ n matrix A is defined as the triple (i/sub +/ (A), i/spl I.bar/(A), i/sub 0/(A)), where i/sub +/(A), i/spl I.bar/(A), and i/sub 0/(A) are the number of eigenvalues of A, counting multiplicities, with positive, negative, and zero real part. It is known that the inertia of a large class of matrices can be determined in PL (probabilistic logspace). However, the general... View full abstract»

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  • Better time-space lower bounds for SAT and related problems

    Publication Year: 2005, Page(s):40 - 49
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (267 KB) | HTML iconHTML

    We make several improvements on time lower bounds for concrete problems in NP and PH. 1) We present an elementary technique based on "indirect diagonalization" that uniformly improves upon the known nonlinear time lower bounds for nondeterminism and alternating computation, on both sublinear (n/sup o(1)/) space RAMs and sequential worktape machines with random access to the input. We obtain better... View full abstract»

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  • A direct sum theorem for corruption and the multiparty NOF communication complexity of set disjointness

    Publication Year: 2005, Page(s):52 - 66
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (307 KB) | HTML iconHTML

    We prove that corruption, one of the most powerful measures used to analyze 2-party randomized communication complexity, satisfies a strong direct sum property under rectangular distributions. This direct sum bound holds even when the error is allowed to be exponentially close to 1. We use this to analyze the complexity of the widely-studied set disjointness problem in the usual "number-on-the-for... View full abstract»

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  • Monotone circuits for weighted threshold functions

    Publication Year: 2005, Page(s):67 - 75
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (238 KB) | HTML iconHTML

    Weighted threshold functions with positive weights are a natural generalization of unweighted threshold functions. These functions are clearly monotone. However, the naive way of computing them is adding the weights of the satisfied variables and checking if the sum is greater than the threshold; this algorithm is inherently non-monotone since addition is a non-monotone function. In this work we b... View full abstract»

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  • The quantum adversary method and classical formula size lower bounds

    Publication Year: 2005, Page(s):76 - 90
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (243 KB) | HTML iconHTML

    We introduce two new complexity measures for Boolean functions, which we name sumPI and maxPI. The quantity sumPI has been emerging through a line of research on quantum query complexity lower bounds via the so-called quantum adversary, culminating with the realization that these many different formulations are in fact equivalent. Given that sumPI turns out to be such a robust invariant of a funct... View full abstract»

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  • More on noncommutative polynomial identity testing

    Publication Year: 2005, Page(s):92 - 99
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (154 KB) | HTML iconHTML

    We continue the study of noncommutative polynomial identity testing initiated by Raz and Shpilka and present efficient algorithms for the following problems in the noncommutative model: polynomial identity testing: The algorithm gets as an input an arithmetic circuit with the promise that the polynomial it computes has small degree (for instance, a circuit of logarithmic depth or an arithmetic for... View full abstract»

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  • New results on the complexity of the middle bit of multiplication

    Publication Year: 2005, Page(s):100 - 110
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (195 KB) | HTML iconHTML

    It is well known that the hardest bit of integer multiplication is the middle bit, i.e., MUL/sub n - 1, n/. This paper contains several new results on its complexity. First, the size s of randomized read-k branching programs, or, equivalently, its space (log s) is investigated. A randomized algorithm for MUL/sub n - 1, n/ with k = O(log n) (implying time O(n log n)), space O(log n) and error proba... View full abstract»

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  • On the Fourier spectrum of symmetric Boolean functions with applications to learning symmetric juntas

    Publication Year: 2005, Page(s):112 - 119
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (152 KB) | HTML iconHTML

    We study the following question: What is the smallest t such that every symmetric Boolean function on k variables (which is not a constant or a parity function), has a non-zero Fourier coefficient of order at least 1 and at most t? We exclude the constant functions for which there is no such t and the parity functions for which t has to be k. Let /spl tau/(k) be the smallest such t. The train cont... View full abstract»

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  • Short PCPs verifiable in polylogarithmic time

    Publication Year: 2005, Page(s):120 - 134
    Cited by:  Papers (21)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (302 KB) | HTML iconHTML

    We show that every language in NP has a probabilistically checkable proof of proximity (i.e., proofs asserting that an instance is "close" to a member of the language), where the verifier's running time is polylogarithmic in the input size and the length of the probabilistically checkable proof is only polylogarithmically larger that the length of the classical proof. (Such a verifier can only que... View full abstract»

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  • Tolerant versus intolerant testing for Boolean properties

    Publication Year: 2005, Page(s):135 - 140
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (148 KB) | HTML iconHTML

    A property tester with high probability accepts inputs satisfying a given property and rejects inputs that are far from satisfying it. A tolerant property tester, as defined by Parnas, Ron and Rubinfeld, must also accept inputs that are close enough to satisfying the property. We construct two properties of binary functions for which there exists a test making a constant number of queries, but yet... View full abstract»

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  • On the hardness of approximating MULTICUT and SPARSEST-CUT

    Publication Year: 2005, Page(s):144 - 153
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (188 KB) | HTML iconHTML

    We show that the MULTICUT, SPARSEST-CUT, and MIN-2CNF/spl equiv/DELETION problems are NP-hard to approximate within every constant factor, assuming the unique games conjecture of Khot [STOC, 2002]. A quantitatively stronger version of the conjecture implies inapproximability factor of /spl Omega/(log log n). View full abstract»

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  • Hardness of Max 3SAT with no mixed clauses

    Publication Year: 2005, Page(s):154 - 162
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (174 KB) | HTML iconHTML

    We study the complexity of approximating Max NM-E3SAT, a variant of Max 3SAT when the instances are guaranteed to not have any mixed clauses, i.e., every clause has either all its literals unnegated or all of them negated. This is a natural special case of Max 3SAT introduced Guruswami (2004), where the question of whether this variant can be approximated within a factor better than 7/8 was also p... View full abstract»

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  • On the sensitivity of cyclically-invariant Boolean functions

    Publication Year: 2005, Page(s):163 - 167
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (129 KB) | HTML iconHTML

    In this paper we construct a cyclically invariant Boolean function whose sensitivity is /spl Theta/(n/sup 1/3/). This result answers nvo previously published questions. Turtin (1984) asked if any Boolean function, invariant under some transitive group of permutations, has sensitivity /spl Omega/(/spl radic/n). Kenyon and Kutin (2004) asked whether for a "nice" function the product of 0-sensitivity... View full abstract»

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  • On the complexity of hardness amplification

    Publication Year: 2005, Page(s):170 - 182
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (233 KB) | HTML iconHTML

    We study the task of transforming a hard function f, with which any small circuit disagrees on (1 - /spl delta/)/2 fraction of the input, into a harder function f', with which any small circuit disagrees on (1 - /spl delta//sup k/)/2 fraction of the input, for /spl delta/ /spl isin/ (0,1) and k /spl isin/ /spl Nopf/. We show that this process cannot be carried out in a black-box way by a circuit o... View full abstract»

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  • On constructing parallel pseudorandom generators from one-way functions

    Publication Year: 2005, Page(s):183 - 197
    Cited by:  Papers (11)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (260 KB) | HTML iconHTML

    We study pseudorandom generator (PRG) constructions G/sup f/ : {0, 1}/sup l/ /spl rarr/ {0, 1}/sup 1+s/ from one-way functions f : {0, 1}/sup n/ /spl rarr/ {0, 1}/sup m/. We consider PRG constructions of the form G/sup f/ (x) = C(f(q/sub 1/) ...f (g/sub poly(n)/)) where C is a polynomial-size constant depth circuit (i.e., AC/sup 0/) and C and the q's are generated from x arbitrarily. We show that ... View full abstract»

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  • Pseudorandom bits for constant depth circuits with few arbitrary symmetric gates

    Publication Year: 2005, Page(s):198 - 209
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (209 KB) | HTML iconHTML

    We exhibit an explicitly computable 'pseudorandom' generator stretching l bits into m(l) = l/sup /spl Omega/(log l)/ bits that look random to constant-depth circuits of size m(l) with log m(l) arbitrary symmetric gates (e.g. PARITY, MAJORITY). This improves on a generator by Luby, Velickovic and Wigderson (ISTCS '93) that achieves the same stretch but only fools circuits of depth 2 with one arbitr... View full abstract»

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