Proceedings 17th IEEE Annual Conference on Computational Complexity

21-24 May 2002

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  • 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
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (186 KB)

    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
  • Lower bounds for linear locally decodable codes and private information retrieval

    Publication Year: 2002, Page(s):143 - 151
    Cited by:  Papers (16)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (412 KB) | HTML iconHTML

    We prove that if a linear error-correcting code C: {0, 1}n → {0, 1}m is such that a bit of the message can be probabilistically reconstructed by looking at two entries of a corrupted codeword, then m = 2Ω(n). We also present several extensions of this result. We show a reduction from the complexity, of one-round, information-theoretic private informatio... View full abstract»

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  • On the complexity of integer multiplication in branching programs with multiple tests and in read-once branching programs with limited nondeterminism

    Publication Year: 2002, Page(s):62 - 71
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (369 KB) | HTML iconHTML

    Branching programs (BPs) are a well-established computation and representation model for Boolean functions. Although exponential lower bounds for restricted BPs such as read-once branching programs (BP1s) have been known for a long time, the proof of lower bounds for important selected functions is sometimes difficult. Especially the complexity of fundamental functions such as integer multiplicati... 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 (11)
    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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  • Streaming computation of combinatorial objects

    Publication Year: 2002, Page(s):133 - 142
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (420 KB) | HTML iconHTML

    We prove (mostly tight) space lower bounds for "streaming" (or "on-line") computations of four fundamental combinatorial objects: error-correcting codes, universal hash functions, extractors, and dispersers. Streaming computations for these objects are motivated algorithmically by massive data set applications and complexity-theoretically by pseudorandomness and derandomization for space-bounded p... View full abstract»

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  • Functions that have read-twice constant width branching programs are not necessarily testable

    Publication Year: 2002, Page(s):55 - 61
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (376 KB) | HTML iconHTML

    We construct a property on 0/1-strings that has a representation by a collection of width 3, read-twice oblivious branching programs, but for which any 2-sided ε-testing algorithm must make at least Ω(n1/10) many queries for some fixed small enough ε. This shows that Newman's result (2000) cannot be generalized to read-k-times functions for k > 1 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 (6)
    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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  • 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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  • Resolution lower bounds for the weak pigeon hole principle

    Publication Year: 2002, Page(s): 3
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (224 KB) | HTML iconHTML

    We prove that any resolution proof for the weak pigeonhole principle, with n holes and any number of pigeons, is of length Ω(2n∈), (for some constant ∈ > 0). One corollary is that a certain propositional formulation of the statement NP ⊄ P/poly does not have short resolution proofs View full abstract»

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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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  • 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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  • 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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  • Learnability beyond AC0

    Publication Year: 2002, Page(s): 16
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (219 KB) | HTML iconHTML

    We give an algorithm for learning a more expressive circuit class than the class AC0 considered by Linial et al. (1993) and Kharitonov (1993). The new algorithm learns constant-depth AND/OR/NOT circuits augmented with (a limited number of) majority gates. Our main positive result for these circuits is stated informally View full abstract»

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  • 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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  • 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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  • Hard examples for bounded depth frege

    Publication Year: 2002, Page(s): 2
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (209 KB) | HTML iconHTML

    First Page of the Article
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  • Pseudorandomness and average-case complexity via uniform reductions

    Publication Year: 2002, Page(s):103 - 112
    Cited by:  Papers (14)
    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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  • Randomness conductors and constant-degree lossless expanders

    Publication Year: 2002, Page(s): 8
    Cited by:  Papers (2)
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  • Better lower bounds for locally decodable codes

    Publication Year: 2002, Page(s):152 - 161
    Cited by:  Papers (7)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (406 KB) | HTML iconHTML

    An error-correcting code is said to be locally decodable if a randomized algorithm can recover any single bit of a message by reading only a small number of symbols of a possibly corrupted encoding of the message. Katz and Trevisan (2000) showed that any such code C: {0, 1} → Σm with a decoding algorithm that makes at most q probes must satisfy m = Ω((n/log |Σ|) View full abstract»

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  • Information theory methods in communication complexity

    Publication Year: 2002, Page(s):72 - 81
    Cited by:  Papers (14)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (395 KB) | HTML iconHTML

    We use tools and techniques from information theory to study communication complexity problems in the one-way and simultaneous communication models. Our results include: (1) a tight characterization of multi-party one-way communication complexity for product distributions in terms of VC-dimension and shatter coefficients; (2) an equivalence of multi-party one-way and simultaneous communication mod... View full abstract»

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