Proceedings 16th Annual IEEE Conference on Computational Complexity

18-21 June 2001

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  • Proceedings 16th Annual IEEE Conference on Computational Complexity [front matter]

    Publication Year: 2001
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    Freely Available from IEEE
  • Author index

    Publication Year: 2001, Page(s): 303
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  • Hausdorff dimension in exponential time

    Publication Year: 2001, Page(s):210 - 217
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (596 KB) | HTML iconHTML

    In this paper we investigate effective versions of Hausdorff dimension which have been recently introduced by Lutz. We focus on dimension in the class E of sets computable in linear exponential time. We determine the dimension of various classes related to fundamental structural properties including different types of autoreducibility and immunity. By a new general invariance theorem for resource-... View full abstract»

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  • Space complexity of random formulae in resolution

    Publication Year: 2001, Page(s):42 - 51
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (624 KB) | HTML iconHTML

    We study the space complexity of refuting unsatisfiable random k-CNFs in the resolution proof system. We prove that for any large enough Δ, with high probability a random k-CNF over n variables and Δn clauses requires resolution clause space of Ω(n·Δ-1+εk-2-ε/), for any 0<ε<1/2. For constant Δ, this gives us linear, optimal, lowe... View full abstract»

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  • Simple analysis of graph tests for linearity and PCP

    Publication Year: 2001, Page(s):244 - 254
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (664 KB) | HTML iconHTML

    We give a simple analysis of the PCP (probabilistically Checkable Proof) with low amortized query complexity of Samorodnitsky and Trevisan (2000). The analysis also applied to the linearity testing over finite fields, giving a better estimate of the acceptance probability in terms of the distance of the tested function to the closest linear function View full abstract»

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  • A stronger Kolmogorov zero-one law for resource-bounded measure

    Publication Year: 2001, Page(s):204 - 209
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (392 KB) | HTML iconHTML

    Resource-bounded measure has been defined on the classes E, E2, ESPACE, E2SPACE, REC, and the class of all languages. It is shown here that if C is any of these classes and X is a set of languages that is closed under finite variations and has outer measure less than 1 in C, then X has measure 0 in C. This result strengthens Lutz's resource-bounded generalization of the class... View full abstract»

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  • Monotone simulations of nonmonotone proofs

    Publication Year: 2001, Page(s):36 - 41
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (416 KB) | HTML iconHTML

    We show that an LK proof of size m of a monotone sequent (a sequent that contains only formulas in the basis ∧, V) can be turned into a proof containing only monotone formulas of size mO(log m) and with the number of proof lines polynomial in m. Also we show that some interesting special cases, namely the functional and the onto versions of PHP and a version of the matching princip... View full abstract»

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  • Time-space tradeoffs in the counting hierarchy

    Publication Year: 2001, Page(s):295 - 302
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (580 KB) | HTML iconHTML

    Extends the lower-bound techniques of L. Fortnow (2000) to the unbounded-error probabilistic model. A key step in the argument is a generalization of V.A. Nepomnjasˇcˇii˘'s (1970) theorem from the Boolean setting to the arithmetic setting. This generalization is made possible due to the recent discovery of logspace-uniform TC0 circuits for iterated multiplication (A. C... View full abstract»

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  • Towards proving strong direct product theorems

    Publication Year: 2001, Page(s):107 - 117
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (808 KB) | HTML iconHTML

    A fundamental question of complexity theory is the direct product question. A famous example is Yao's (1982) XOR-lemma, in which one assumes that some function f is hard on average for small circuits, (meaning that every circuit of some fixed size s which attempts to compute f is wrong on a non-negligible fraction of the inputs) and concludes that every circuit of size s' has a small advantage ove... View full abstract»

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  • Links between complexity theory and constrained block coding

    Publication Year: 2001, Page(s):226 - 243
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1424 KB) | HTML iconHTML

    The goal of this paper is to establish links between computational complexity theory and the theory and practice of constrained block coding. The complexities of several fundamental problems in constrained block coding are shown to be complete in various classes of the existing complexity-theoretic structure. The results include (relatively rare) Σ2p-, Σ3 View full abstract»

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  • In search of an easy witness: exponential time vs. probabilistic polynomial time

    Publication Year: 2001, Page(s):2 - 12
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (820 KB) | HTML iconHTML

    Restricting the search space {0, 1}n to the set of truth tables of “easy” Boolean functions on log n variables, as well as using some known hardness-randomness tradeoffs, we establish a number of results relating the complexity of exponential-time and probabilistic polynomial-time complexity classes. In particular, we show that NEXP⊂P/poly⇔NEXP=MA; this can be inter... View full abstract»

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  • On the power of nonlinear secret-sharing

    Publication Year: 2001, Page(s):188 - 202
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1148 KB) | HTML iconHTML

    A secret-sharing scheme enables a dealer to distribute a secret among no parties such that only some predefined authorized sets of parties will be able to reconstruct the secret from their shares. The (monotone) collection of authorized sets is called an access structure, and is freely identified with its characteristic monotone function f: {0, 1}n→{0, 1}. A family of secret-sharin... View full abstract»

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  • Comparing notions of full derandomization

    Publication Year: 2001, Page(s):28 - 34
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (464 KB) | HTML iconHTML

    Most of the hypotheses of full derandomization fall into two sets of equivalent statements: those equivalent to the existence of efficient pseudorandom generators and those equivalent to approximating the accepting probability of a circuit. We give the first relativized world where these sets of equivalent statements are not equivalent to each other View full abstract»

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  • On separators, segregators and time versus space

    Publication Year: 2001, Page(s):286 - 294
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (704 KB) | HTML iconHTML

    Gives an extension of the result due to Paul, Pippenger, Szemeredi and Trotter (1983) that deterministic linear time (DTIME) is distinct from nondeterministic linear time (NTIME). We show that NTIME[n√log*(n)] ≠ DTIME[n√log*(n)]. We show that if the class of multi-pushdown graphs has {o(n), o[n/log(n)]} segregators, then NTIME[n log(n)] ≠ DTIME[n log(n)]. We also show that at lea... View full abstract»

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  • A linear lower bound on the unbounded error probabilistic communication complexity

    Publication Year: 2001, Page(s):100 - 106
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (472 KB) | HTML iconHTML

    We prove a general lower bound on the complexity of unbounded error probabilistic communication protocols. This result improves on a lower bound for bounded error protocols from Krause (1996). As a simple consequence we get the, to our knowledge, first linear lower bound on the complexity of unbounded error probabilistic communication protocols for the functions defined by Hadamard matrices. We al... View full abstract»

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  • On the non-approximability of Boolean functions by OBDDs and read-k-times branching programs

    Publication Year: 2001, Page(s):172 - 183
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (812 KB) | HTML iconHTML

    Branching problems are considered as a nonuniform model of computation in complexity theory as well as a data structure for boolean functions in several applications. In many applications (e.g., verification), exact representations are required. For learning boolean functions f on the basis of classified examples, it is sufficient to produce the representation of a function g approximating f. This... View full abstract»

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  • On the complexity of approximating the VC dimension

    Publication Year: 2001, Page(s):220 - 225
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (420 KB) | HTML iconHTML

    We study the complexity of approximating the VC dimension of a collection of sets, when the sets are encoded succinctly by a small circuit. We show that this problem is: Σ3p-hard to approximate to within a factor 2-ε for any ε>0; approximable in Aℳ to within a factor 2; and Aℳ-hard to approximate to within a factor Nε for some cons... View full abstract»

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  • Resolution complexity of independent sets in random graphs

    Publication Year: 2001, Page(s):52 - 68
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1204 KB) | HTML iconHTML

    We consider the problem of providing a resolution proof of the statement that a given graph with n vertices and Δn edges does not contain an independent set of size k. For randomly chosen graphs with constant Δ, we show that such proofs almost surely require size exponential in n. Further, for Δ=o(n1/5) and any k⩽n/5, we show that these proofs almost surely require... View full abstract»

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  • Logical operations and Kolmogorov complexity. II

    Publication Year: 2001, Page(s):256 - 265
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (676 KB) | HTML iconHTML

    For Part I, see Theoretical Computer Science (to be published). Investigates the Kolmogorov complexity of the problem (a→c)∧(b→d), defined as the minimum length of a program that, given a, outputs c and, given b, outputs d. We prove that, unlike all known problems of this kind, its complexity is not expressible in terms of the Kolmogorov complexity of a, b, c and d, their pairs, trip... View full abstract»

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  • Communication complexity lower bounds by polynomials

    Publication Year: 2001, Page(s):120 - 130
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (856 KB) | HTML iconHTML

    The quantum version of communication complexity allows the two communicating parties to exchange qubits and/or to make use of prior entanglement (shared EPR-pairs). Some lower bound techniques are available for qubit communication complexity, but except for the inner product function, no bounds are known for the model with unlimited prior entanglement. We show that the “log rank” lower... View full abstract»

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  • Towards uniform AC0-isomorphisms

    Publication Year: 2001, Page(s):13 - 20
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (616 KB) | HTML iconHTML

    For any class C closed under NC1 reductions, it is shown that all sets complete for C under logspace-uniform AC0 reductions are isomorphic under logspace-uniform AC0-computable isomorphisms View full abstract»

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  • Lower bounds for approximations by low degree polynomials over Z m

    Publication Year: 2001, Page(s):184 - 187
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (248 KB) | HTML iconHTML

    We use a Ramsey-theoretic argument to obtain the first lower bounds for approximations over Zm by nonlinear polynomials: (i) A degree-2 polynomial over Zm (m odd) must differ from the parity function on at least a 1/2-1/2((log n)Ω(1)) fraction of all points in the Boolean n-cube. A degree-O(1) polynomial over Zm (m odd) must differ from the parity ... View full abstract»

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  • Tree resolution proofs of the weak pigeon-hole principle

    Publication Year: 2001, Page(s):69 - 75
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (500 KB) | HTML iconHTML

    We prove that any optimal tree resolution proof of PHPn m is of size 2θ(n log n), independently from m, even if it is infinity. So far, only a 2Ω(n) lower bound has been known in the general case. We also show that any, not necessarily optimal, regular tree resolution proof PHPn m is bounded by 2O(n log m). To... View full abstract»

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  • Computational depth

    Publication Year: 2001, Page(s):266 - 273
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (520 KB) | HTML iconHTML

    Introduces computational depth, a measure for the amount of “non-random” or “useful” information in a string, by considering the difference of various Kolmogorov complexity measures. We investigate three instantiations of computational depth: (1) basic computational depth, a clean notion capturing the spirit of C.H. Bennett's (1988) logical depth; (2) time-t computational d... View full abstract»

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  • Quantum algorithms for element distinctness

    Publication Year: 2001, Page(s):131 - 137
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (564 KB) | HTML iconHTML

    We present several applications of quantum amplitude amplification to finding claws and collisions in ordered or unordered functions. Our algorithms generalize those of Brassard, Hoyer, and Tapp (1998), and imply an O(N3/4 log N) quantum upper bound for the element distinctness problem in the comparison complexity model. This contrasts with Θ(N log N) classical complexity. We also... View full abstract»

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