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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  • Author index

    Publication Year: 2001, Page(s): 303
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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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  • Quantum algorithmic entropy

    Publication Year: 2001, Page(s):274 - 283
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (676 KB) | HTML iconHTML

    Extends algorithmic information theory to quantum mechanics, taking a universal semi-computable density matrix (“universal probability”) as a starting point, and defines complexity (an operator) as its negative logarithm. A number of properties of Kolmogorov complexity extend naturally to the new domain. Approximately, a quantum state is simple if it is within a small distance from a l... 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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  • Uniform circuits for division: consequences and problems

    Publication Year: 2001, Page(s):150 - 159
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (756 KB) | HTML iconHTML

    Integer division has been known to lie in P-uniform TC0 since the mid-1980s, and recently this was improved to L-uniform TC0. 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 TC0 (also known as FOM). We obtain tight bounds on the uniformity required for division... 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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  • Separation of NP-completeness notions

    Publication Year: 2001, Page(s):78 - 89
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (708 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 ⩽T P-complete but not ⩽ttP-complete. We provide fairly thorough analyses of the hypotheses that we introduce 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 (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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  • Quantum versus classical learnability

    Publication Year: 2001, Page(s):138 - 148
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (844 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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  • 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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  • 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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  • 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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  • 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 (500 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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  • 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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  • 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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  • 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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  • Affine projections of symmetric polynomials

    Publication Year: 2001, Page(s):160 - 171
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (684 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-Smd(l1, l2, …, lm) (Smd is the d'th elementary symmetric polynomial in m variables, and the li's are linea... 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 (544 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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  • 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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  • 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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  • 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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  • 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 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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  • 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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