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Proceedings 17th IEEE Annual Conference on Computational Complexity

21-24 May 2002

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Displaying Results 1 - 25 of 38
  • Proceedings 17th IEEE Annual Conference on Computational Complexity [front matter]

    Publication Year: 2002
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    Freely Available from IEEE
  • 3-MANIFOLD KNOT GENUS is NP-complete

    Publication Year: 2002
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (193 KB)

    Summary form only given, as follows. One of the central questions in topology is determining whether a given curve is knotted or unknotted. An algorithm to decide this question was given by Haken (1961), using the technique of normal surfaces. These surfaces are rigid, discretized surfaces, well suited for algorithmic analysis. Any oriented surface without boundary can be obtained from a sphere by... View full abstract»

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  • The history of complexity

    Publication Year: 2002
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (195 KB) | HTML iconHTML

    Summary form only given. We describe several trends in the history of computational complexity, including: the early history of complexity; the development of NP-completeness and the structure of complexity classes; how randomness, parallelism and quantum mechanics has forced us to reexamine our notions of efficient computation and how computational complexity has responded to these new models; th... View full abstract»

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  • Rapid mixing

    Publication Year: 2002
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    Summary form only given. In the past decade many proofs of tractability, have involved showing that some Markov chain "mixes rapidly". We do a fast tour of the highlights of Markov chain mixing, with a view toward answering, or at least addressing, the following questions: What is rapid mixing? How do you prove it, and why would you want to? Does it really have anything to do with computational co... View full abstract»

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  • Author index

    Publication Year: 2002, Page(s): 172
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    Freely Available from IEEE
  • On communication over an entanglement-assisted quantum channel

    Publication Year: 2002, Page(s): 12
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (213 KB) | HTML iconHTML

    Shared entanglement is a resource available to parties communicating over a quantum channel, much akin to public coins in classical communication protocols: the two parties may be given some number of quantum bits jointly prepared in a fixed superposition, prior to communicating with each other. The quantum channel is then said to be "entanglement-assisted." Shared randomness does not help in the ... View full abstract»

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  • Time-space tradeoffs, multiparty communication complexity, and nearest-neighbor problems

    Publication Year: 2002, Page(s): 11
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (223 KB) | HTML iconHTML

    The first non-trivial time-space tradeoff lower bounds have been shown for decision problems in P using notions derived from the study of two-party communication complexity. These results are proven directly for branching programs, natural generalizations of decision trees to directed graphs that provide elegant models of both non-uniform time T and space S simultaneously. We develop a new lower b... View full abstract»

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  • Sampling short lattice vectors and the closest lattice vector problem

    Publication Year: 2002, Page(s):41 - 45
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (307 KB) | HTML iconHTML

    We present a 2O(n) time Turing reduction from the closest lattice vector problem to the shortest lattice vector problem. Our reduction assumes access to a subroutine that solves SVP exactly and a subroutine to sample short vectors from a lattice, and computes a (1+ε)-approximation to CVP As a consequence, using the SVP algorithm from (Ajtai et al., 2001), we obtain a randomized 2[O... View full abstract»

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  • Decoding concatenated codes using soft information

    Publication Year: 2002, Page(s):122 - 131
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (367 KB) | HTML iconHTML

    We present a decoding algorithm for concatenated codes when the outer code is a Reed-Solomon code and the inner code is arbitrary. "Soft" information on the reliability of various symbols is passed by the inner decodings and exploited in the Reed-Solomon decoding. This is the first analysis of such a soft algorithm that works for arbitrary inner codes; prior analyses could only, handle some specia... View full abstract»

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  • The complexity of approximating the entropy

    Publication Year: 2002, Page(s): 10
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (225 KB) | HTML iconHTML

    The Shannon entropy is a measure of the randomness of a distribution, and plays a central role in statistics, information theory, and data compression. Knowing the entropy of a random source can shed light on the compressibility of data produced by such a source. We consider the complexity of approximating the entropy under various different assumptions on the way the input is presented View full abstract»

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  • The inapproximability of lattice and coding problems with preprocessing

    Publication Year: 2002, Page(s):32 - 40
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (383 KB) | HTML iconHTML

    We prove that the closest vector problem with preprocessing (CVPP) is NP-hard to approximate within any factor less than √5/3. More specifically, we show that there exists a reduction from an NP-hard problem to the approximate closest vector problem such that the lattice depends only on the size of the original problem, and the specific instance is encoded solely, in the target vector. It fo... View full abstract»

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  • Algorithmic derandomization via complexity theory

    Publication Year: 2002, Page(s): 6
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (194 KB) | HTML iconHTML

    First Page of the Article
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  • Pseudo-random generators and structure of complete degrees

    Publication Year: 2002, Page(s):113 - 121
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (365 KB) | HTML iconHTML

    It is shown that, if there exist sets in E (the exponential complexity class) that require 2Ω(n)-sized circuits, then sets that are hard for class P (the polynomial complexity class) and above, under 1-1 reductions, are also hard under 1-1 size-increasing reductions. Under the assumption of the hardness of solving the RSA (Rivest-Shamir-Adleman, 1978) problem or the discrete log p... View full abstract»

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  • On the power of unique 2-prover 1-round games

    Publication Year: 2002, Page(s): 15
    Cited by:  Papers (32)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (209 KB) | HTML iconHTML

    A 2-prover game is called unique if the answer of one prover uniquely determines the answer of the second prover and vice versa (we implicitly assume games to be one round games). The value of a 2-prover game is the maximum acceptance probability of the verifier over all the prover strategies. We make a conjecture regarding the power of unique 2-prover games, which we call the Unique Games Conject... View full abstract»

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  • Resolution lower bounds for the weak pigeonhole principle

    Publication Year: 2002, Page(s): 1
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (222 KB) | HTML iconHTML

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  • Expanders from symmetric codes

    Publication Year: 2002, Page(s): 9
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (264 KB) | HTML iconHTML

    A set S in the vector space Fpn is "good" if it satisfies any of the following (almost) equivalent conditions: (1) S are the rows of a generating matrix for a linear distance code, (2) all (nontrivial) Fourier coefficients of S are bounded away from 1, and (3) the Cayley graph on Fp n with generators S is a good expander A good set S mu... View full abstract»

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  • Resolution width-size trade-offs for the Pigeon-Hole Principle

    Publication Year: 2002, Page(s):27 - 31
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (315 KB) | HTML iconHTML

    We prove the following two results: (1) There is a resolution proof of the Weak Pigeon-Hole Principle, WPHPnmof size 2O([n log n/log m]+log m) for any number of pigeons m and any number of holes n. (2) Any resolution proof of WPHPn m of width (1/16 - ε) n2 has to be of size 2 Ω(n), independently from m.. These ... View full abstract»

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  • Improved cryptographic hash functions with worst-case/average-case connection

    Publication Year: 2002, Page(s): 5
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (214 KB) | HTML iconHTML

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  • Universal arguments and their applications

    Publication Year: 2002, Page(s):162 - 171
    Cited by:  Papers (18)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (417 KB) | HTML iconHTML

    We put forward a new type of computationally-sound proof systems, called universal-arguments, which are related but different from both CS-proofs (as defined by Micali, 2000) and arguments (as defined by Brassard et al., 1986). In particular, we adopt the instance-based prover-efficiency paradigm of CS-proofs, but follow the computational-soundness condition of argument systems (i.e., we consider ... View full abstract»

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  • Algebras of minimal rank over perfect fields

    Publication Year: 2002, Page(s):92 - 101
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (410 KB) | HTML iconHTML

    Let R(A) denote the rank (also called the bilinear complexity) of a finite-dimensional associative algebra A. A fundamental lower bound for R(A) is the so-called Alder-Strassen (1981) bound: R(A) ⩾ 2 dim A-t, where t is the number of maximal two-sided ideals of A. The class of algebras for which the Alder-Strassen bound is sharp, the so-called "algebras of minimal rank", has received wide atte... View full abstract»

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  • Hardness amplification within NP

    Publication Year: 2002, Page(s): 13
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (232 KB) | HTML iconHTML

    We investigate whether, if NP is slightly hard on average, it is very hard on average View full abstract»

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  • The correlation between parity and quadratic polynomials mod 3

    Publication Year: 2002, Page(s):47 - 54
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (358 KB) | HTML iconHTML

    We prove exponentially small upper bounds on the correlation between parity and quadratic polynomials mod 3. One corollary of this is that in order to compute parity, circuits consisting of a threshold gate at the top, mod 3 gates in the middle, and AND gates of fan-in two at the inputs must be of size 2Ω(n). This is the first result of this type for general mod subcircuits with A... View full abstract»

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  • Arthur and Merlin in a quantum world

    Publication Year: 2002, Page(s): 132
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (201 KB) | HTML iconHTML

    Arthur does not have a lot of time to spend performing difficult computations. He's recently obtained a quantum computer, but often it seems not to help - he only has a few quantum algorithms, and Merlin maintains that there aren't any other interesting ones, so Merlin is forced to convince the untrusting Arthur of the truth of various facts. However, Arthur and Merlin have a new resource at their... View full abstract»

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  • Pseudo-random generators for all hardnesses

    Publication Year: 2002, Page(s): 7
    Cited by:  Papers (1)
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  • Pseudorandomness and average-case complexity via uniform reductions

    Publication Year: 2002, Page(s):103 - 112
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (362 KB)

    Impagliazzo and Wigderson (1998) gave the first construction of pseudorandom generators from a uniform complexity assumption on EXP (namely EXP = BPP). Unlike results in the nonuniform setting, their result does not provide a continuous trade-off between worst-case hardness and pseudorandomness, nor does it explicitly establish an average-case hardness result. ... View full abstract»

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