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Proceedings 16th Annual IEEE Conference on Computational Complexity

18-21 June 2001

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Displaying Results 1 - 25 of 32
  • Proceedings 16th Annual IEEE Conference on Computational Complexity [front matter]

    Publication Year: 2001
    Request permission for commercial reuse | PDF file iconPDF (181 KB)
    Freely Available from IEEE
  • 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 (979 KB) | HTML iconHTML

    Restricting the search space {0, 1}/sup 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/spl sub/P/poly/spl hArr/NEXP=MA; this can be interpreted to... View full abstract»

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  • Towards uniform AC/sup 0/-isomorphisms

    Publication Year: 2001, Page(s):13 - 20
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (735 KB) | HTML iconHTML

    For any class C closed under NC/sup 1/ reductions, it is shown that all sets complete for C under logspace-uniform AC/sup 0/ reductions are isomorphic under logspace-uniform AC/sup 0/-computable isomorphisms. View full abstract»

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  • Universal traversal sequences with backtracking

    Publication Year: 2001, Page(s):21 - 27
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (609 KB) | HTML iconHTML

    We introduce a new notion of traversal sequences that we call exploration sequences. Exploration sequences share many properties with the traversal sequences defined in (AKL+), but they also exhibit some new properties. In particular, they have an ability to backtrack, and their random properties are robust under choice of the probability distribution on labels. Further, we present extremely simpl... 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 (551 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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  • Monotone simulations of nonmonotone proofs

    Publication Year: 2001, Page(s):36 - 41
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (509 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 /spl and/, V) can be turned into a proof containing only monotone formulas of size m/sup O(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 principle... 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 (753 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 /spl Delta/, with high probability a random k-CNF over n variables and /spl Delta/n clauses requires resolution clause space of /spl Omega/(n/spl middot//spl Delta//sup -1+/spl epsiv//k-2-/spl epsiv//), for any 0</spl epsiv/<1/2. For constant /spl Delta/, t... 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 (1447 KB) | HTML iconHTML

    We consider the problem of providing a resolution proof of the statement that a given graph with n vertices and /spl Delta/n edges does not contain an independent set of size k. For randomly chosen graphs with constant /spl Delta/, we show that such proofs almost surely require size exponential in n. Further, for /spl Delta/=o(n/sup 1/5/) and any k/spl les/n/5, we show that these proofs almost sur... 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 (605 KB) | HTML iconHTML

    We prove that any optimal tree resolution proof of PHP/sub n//sup m/ is of size 2/sup /spl theta/(n log n)/, independently from m, even if it is infinity. So far, only a 2/sup /spl Omega/(n)/ lower bound has been known in the general case. We also show that any, not necessarily optimal, regular tree resolution proof PHP/sub n//sup m/ is bounded by 2/sup O(n log m)/. To the best of our knowledge, t... View full abstract»

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  • Separation of NP-completeness notions

    Publication Year: 2001, Page(s):78 - 89
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (851 KB) | HTML iconHTML

    We use hypotheses of structural complexity theory to separate various NP-completeness notions. In particular, we introduce a hypothesis from which we describe a set in NP that is /spl les//sub T//sup P/-complete but not /spl les//sub tt//sup P/-complete. We provide fairly thorough analyses of the hypotheses that we introduce. View full abstract»

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  • Bounded query functions with limited output bits

    Publication Year: 2001, Page(s):90 - 98
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (661 KB) | HTML iconHTML

    The paper explores the difference between parallel and serial queries to an NP-complete oracle, SAT, from the perspective of functions with a limited number of output bits. For polynomial-time bounded query language classes, which can be considered as functions with 1 bit output, previous work has shown that 2 serial queries to SAT is equivalent to 3 parallel queries to SAT. In contrast, for funct... 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 (569 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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  • 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 (963 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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  • 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 (1024 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 bound exten... 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 (678 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(N/sup 3/4/ log N) quantum upper bound for the element distinctness problem in the comparison complexity model. This contrasts with /spl Theta/(N log N) classical complexity. We also ... View full abstract»

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  • Quantum versus classical learnability

    Publication Year: 2001, Page(s):138 - 148
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1011 KB) | HTML iconHTML

    Motivated by work on quantum black-box query complexity, we consider quantum versions of two well-studied models of learning Boolean functions: Angluin's (1988) model of exact learning from membership queries and Valiant's (1984) Probably Approximately Correct (PAC) model of learning from random examples. For each of these two learning models we establish a polynomial relationship between the numb... View full abstract»

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  • Uniform circuits for division: consequences and problems

    Publication Year: 2001, Page(s):150 - 159
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (906 KB) | HTML iconHTML

    Integer division has been known to lie in P-uniform TC/sup 0/ since the mid-1980s, and recently this was improved to L-uniform TC/sup 0/. At the time that the results in this paper were proved and submitted for conference presentation, it was unknown whether division lay in DLOGTIME-uniform TC/sup 0/ (also known as FOM). We obtain tight bounds on the uniformity required for division, by showing th... View full abstract»

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  • Affine projections of symmetric polynomials

    Publication Year: 2001, Page(s):160 - 171
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (829 KB) | HTML iconHTML

    We introduce a new model for computing polynomials-a depth 2 circuit with a symmetric gate at the top and plus gates at the bottom, i.e. the circuit computes a symmetric function in linear functions-S/sub m//sup d/(l/sub 1/, l/sub 2/, ..., l/sub m/) (S/sub m//sup d/ is the d'th elementary symmetric polynomial in m variables, and the l/sub i/'s are linear functions). We refer to this model as the s... 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 (982 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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  • Lower bounds for approximations by low degree polynomials over Z/sub m/

    Publication Year: 2001, Page(s):184 - 187
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (304 KB) | HTML iconHTML

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

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  • On the power of nonlinear secret-sharing

    Publication Year: 2001, Page(s):188 - 202
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1370 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}/sup n//spl rarr/{0, 1}. A family of secret-sharing... 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 (484 KB) | HTML iconHTML

    Resource-bounded measure has been defined on the classes E, E/sub 2/, ESPACE, E/sub 2/SPACE, 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 classical Kolmo... View full abstract»

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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 (715 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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  • 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 (513 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: /spl Sigma//sub 3//sup p/-hard to approximate to within a factor 2-/spl epsiv/ for any /spl epsiv/>0; approximable in A/spl Mscr/ to within a factor 2; and A/spl Mscr/-hard to approximate to within a factor N/sup /spl epsiv// f... 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 (1712 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) /spl Sigma//sub 2//sup p/-, /spl Sigma//sub 3//sup ... View full abstract»

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