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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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  • Author index

    Publication Year: 2002, Page(s): 172
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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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  • 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 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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  • 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 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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  • Better lower bounds for locally decodable codes

    Publication Year: 2002, Page(s):152 - 161
    Cited by:  Papers (5)  |  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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  • 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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  • 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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  • Hard examples for bounded depth frege

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

    First Page of the Article
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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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  • The history of complexity

    Publication Year: 2002, Page(s): 46
    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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  • On communication over an entanglement-assisted quantum channel

    Publication Year: 2002, Page(s): 12
    Cited by:  Papers (4)
    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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  • 3-MANIFOLD KNOT GENUS is NP-complete

    Publication Year: 2002, Page(s): 14
    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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  • Lower bounds for linear locally decodable codes and private information retrieval

    Publication Year: 2002, Page(s):143 - 151
    Cited by:  Papers (13)
    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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  • Resolution lower bounds for perfect matching principles

    Publication Year: 2002, Page(s):17 - 26
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (390 KB) | HTML iconHTML

    For an arbitrary hypergraph H let PM(H) be the propositional formula asserting that H contains a perfect matching. We show that every resolution refutation of PM(H) must have size exp((Ω(δ(H)/λ(H)r(H)(log n(H))(r(H)+log n(H)))), where n(H) is the number of vertices, δ(H) is the minimal degree of a vertex, r(H) is the maximal size of an edge, and λ(H) is the maximal ... View full abstract»

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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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  • 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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  • 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

    First Page of the Article
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  • Randomness conductors and constant-degree lossless expanders

    Publication Year: 2002, Page(s): 8
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (210 KB) | HTML iconHTML

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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 (7)
    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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  • Time-space tradeoffs, multiparty communication complexity, and nearest-neighbor problems

    Publication Year: 2002, Page(s): 11
    Cited by:  Papers (1)
    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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  • 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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