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Computational Complexity, 2004. Proceedings. 19th IEEE Annual Conference on

Date 21-24 June 2004

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Displaying Results 1 - 25 of 40
  • Compression of samplable sources

    Publication Year: 2004 , Page(s): 1 - 14
    Cited by:  Papers (2)
    Request Permissions | Click to expandAbstract | PDF file iconPDF (392 KB) |  | HTML iconHTML  

    We study the compression of polynomially samplable sources. In particular, we give efficient prefix-free compression and decompression algorithms for three classes of such sources (whose support is a subset of {0, l}n). 1) We show how to compress sources X samplable by logspace machines to expected length H(X) + O(1). Our next results concern flat sources whose support is in P. 2) If H(... View full abstract»

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  • Some results on majority quantifiers over words

    Publication Year: 2004 , Page(s): 123 - 129
    Cited by:  Papers (2)
    Request Permissions | Click to expandAbstract | PDF file iconPDF (321 KB) |  | HTML iconHTML  

    The class of languages definable by majority quantifiers using the order predicate is investigated. It is shown that the additional use of first order or counting quantifiers does not increase this class. Further on, addition is in this connection a definable numerical predicate, while the converse does not hold. The emptiness problem for this class turns out to be undecidable. View full abstract»

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  • Polynomials that sign represent parity and Descartes rule of signs

    Publication Year: 2004 , Page(s): 223 - 235
    Request Permissions | Click to expandAbstract | PDF file iconPDF (626 KB) |  | HTML iconHTML  

    We study the sparsity of real polynomials that sign represent parity on n variables, each of which takes values from some finite subset A of integers. While the degree of such polynomials has been well studied by M. Minsky and S. Papert (1968) and J. Aspnes (1994), relatively little is known about their sparsity. We study this problem using Descartes rule of signs, a classical result in algebra, r... View full abstract»

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  • Multiparty quantum coin flipping

    Publication Year: 2004 , Page(s): 250 - 259
    Cited by:  Papers (2)
    Request Permissions | Click to expandAbstract | PDF file iconPDF (326 KB) |  | HTML iconHTML  

    We investigate coin-flipping protocols for multiple parties in a quantum broadcast setting: (1) we propose and motivate a definition for quantum broadcast. Our model of quantum broadcast channel is new. (2) We discovered that quantum broadcast is essentially a combination of pairwise quantum channels and a classical broadcast channel. This is a somewhat surprising conclusion, but helps us in both ... View full abstract»

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  • Polylogarithmic-round interactive proofs for coNP collapse the exponential hierarchy

    Publication Year: 2004 , Page(s): 82 - 90
    Request Permissions | Click to expandAbstract | PDF file iconPDF (318 KB) |  | HTML iconHTML  

    It is known (Boppana et a;., 1987) that if every language in coNP has a constant-round interactive proof system, then the polynomial hierarchy collapses. On the other hand, Lund et al. (1992) have shown that #SAT, the #P-complete function that outputs the number of satisfying assignments of a Boolean formula, can be computed by a linear-round interactive protocol. As a consequence, the coNP-comple... View full abstract»

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  • On the power of quantum proofs

    Publication Year: 2004 , Page(s): 260 - 274
    Cited by:  Papers (3)
    Request Permissions | Click to expandAbstract | PDF file iconPDF (450 KB) |  | HTML iconHTML  

    We study the power of quantum proofs, or more precisely, the power of quantum Merlin-Arthur (QMA) protocols, in two well studied models of quantum computation: the black box model and the communication complexity model. Our main results are obtained for the communication complexity model. For this model, we identify a complete promise problem for QMA protocols, the linear sub-spaces distance probl... View full abstract»

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  • Partial bi-immunity and NP-completeness

    Publication Year: 2004 , Page(s): 198 - 203
    Request Permissions | Click to expandAbstract | PDF file iconPDF (382 KB) |  | HTML iconHTML  

    The Turing and many-one completeness notions for NP have been previously separated under measure, genericity, and bi-immunity hypotheses on NP. The proofs of all these results rely on the existence of a language in NP with almost everywhere hardness. In this paper we separate the same NP-completeness notions under a partial bi-immunity hypothesis that is weaker and only yields a language in NP tha... View full abstract»

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  • The complexity of treelike systems over λ-local formulae

    Publication Year: 2004 , Page(s): 68 - 74
    Request Permissions | Click to expandAbstract | PDF file iconPDF (618 KB) |  | HTML iconHTML  

    We describe a system LK(c[λ]) for refuting CNF formulae, as a restriction of the sequent calculus in which every formula in a sequent is defined over at most λ variables. This further generalizes the system Res(k), a generalization of Resolution to k-DNF introduced in (Krajicek, 2001). We adapt the Pudlak-Impagliazzo game (Pudlak and Impagliazzo, 2000) to prove lower bounds for treel... View full abstract»

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  • Quantum Arthur-Merlin games

    Publication Year: 2004 , Page(s): 275 - 285
    Cited by:  Papers (1)
    Request Permissions | Click to expandAbstract | PDF file iconPDF (584 KB) |  | HTML iconHTML  

    This paper studies quantum Arthur-Merlin games, which are a restricted form of quantum interactive proof system in which the verifier's messages are given by unbiased coin-flips. The following results are proved. For one-message quantum Arthur-Merlin games, which correspond to the complexity class QMA, completeness and soundness errors can be reduced exponentially without increasing the length of ... View full abstract»

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  • Consequences and limits of nonlocal strategies

    Publication Year: 2004 , Page(s): 236 - 249
    Cited by:  Papers (20)
    Request Permissions | Click to expandAbstract | PDF file iconPDF (664 KB) |  | HTML iconHTML  

    This paper investigates various aspects of the nonlocal effects that can arise when entangled quantum information is shared between two parties. A natural framework for studying nonlocality is that of cooperative games with incomplete information, where two cooperating players may share entanglement. Here, nonlocality can be quantified in terms of the values of such games. We review some examples ... View full abstract»

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  • Properties of NP-complete sets

    Publication Year: 2004 , Page(s): 184 - 197
    Request Permissions | Click to expandAbstract | PDF file iconPDF (393 KB) |  | HTML iconHTML  

    We study several properties of sets that are complete for NP. We prove that if L is an NP-complete set and S /spl nsupe/ L is a p-selective sparse set, then L -S is ≤mp-hard for NP. We demonstrate existence of a sparse set S ∈ DTIME(22n) such that for every L ∈ NP - P, L - S is not ≤mp-hard for NP. Moreover, we prove for every ... View full abstract»

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  • Computing in fault tolerance broadcast networks

    Publication Year: 2004 , Page(s): 113 - 122
    Cited by:  Papers (5)
    Request Permissions | Click to expandAbstract | PDF file iconPDF (499 KB) |  | HTML iconHTML  

    We consider a fault tolerance broadcast network of n processors each holding one bit of information. The goal is to compute a given Boolean function on the n bits. In each step, a processor may broadcast one bit of information. Each listening processor receives the bit that was broadcasted with error probability bounded by a fixed constant ε. The errors in different steps, as well as for diff... View full abstract»

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  • Lower bounds for randomized and quantum query complexity using Kolmogorov arguments

    Publication Year: 2004 , Page(s): 294 - 304
    Cited by:  Papers (2)
    Request Permissions | Click to expandAbstract | PDF file iconPDF (379 KB) |  | HTML iconHTML  

    We prove a very general lower bound technique for quantum and randomized query complexity, that is easy to prove as well as to apply. To achieve this, we introduce the use of Kolmogorov complexity to query complexity. Our technique generalizes the weighted, unweighted methods of Ambainis, and the spectral method of Barnum, Saks and Szegedy. As an immediate consequence of our main theorem, it can b... View full abstract»

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  • Lower bounds for testing bipartiteness in dense graphs

    Publication Year: 2004 , Page(s): 75 - 81
    Cited by:  Papers (1)
    Request Permissions | Click to expandAbstract | PDF file iconPDF (337 KB) |  | HTML iconHTML  

    We consider the problem of testing bipartiteness in the adjacency matrix model. The best known algorithm, due to Alon and Krivelevich, distinguishes between bipartite graphs and graphs that are ε-far from bipartite using 0(1/ε2) queries. We show that this is optimal for non-adaptive algorithms, up to polylogarithmic factors. We also show a lower bound of Ω(1/ε... View full abstract»

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  • Language compression and pseudorandom generators

    Publication Year: 2004 , Page(s): 15 - 28
    Request Permissions | Click to expandAbstract | PDF file iconPDF (1105 KB) |  | HTML iconHTML  

    The language compression problem asks for succinct descriptions of the strings in a language A such that the strings can be efficiently recovered from their description when given a membership oracle for A. We study randomized and nondeterministic decompression schemes and investigate how close we can get to the information theoretic lower bound of log ||A= n|| for the description lengt... View full abstract»

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  • On pseudoentropy versus compressibility

    Publication Year: 2004 , Page(s): 29 - 41
    Cited by:  Papers (3)
    Request Permissions | Click to expandAbstract | PDF file iconPDF (1273 KB) |  | HTML iconHTML  

    A source is comprehensible if we can efficiently compute short descriptions of strings in the support and efficiently recover the strings from the descriptions. A source has high pseudo-entropy if it is computationally distinguishable from a source of high entropy. In this paper, we present a technique for proving lower bounds on compressibility in an oracle setting, which yields the following res... View full abstract»

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  • Solvable group isomorphism is (almost) in NP ∩ CoNP

    Publication Year: 2004 , Page(s): 91 - 103
    Request Permissions | Click to expandAbstract | PDF file iconPDF (438 KB) |  | HTML iconHTML  

    The group isomorphism problem consists in deciding whether two input groups G1 and G2 given by their multiplication tables are isomorphic. We first give a 2-round Arthur-Merlin protocol for the group non-isomorphism problem such that on input groups (G1, G2) of size n, Arthur uses O(log6 n) random bits and Merlin uses O(log2 n) nond... View full abstract»

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  • Towards the classical communication complexity of entanglement distillation protocols with incomplete information

    Publication Year: 2004 , Page(s): 305 - 319
    Request Permissions | Click to expandAbstract | PDF file iconPDF (480 KB) |  | HTML iconHTML  

    Entanglement is an essential resource for quantum communication and quantum computation, similar to shared random bits in the classical world. Entanglement distillation extracts nearly-perfect entanglement from imperfect entangled state. The classical communication complexity of these protocols is the minimal amount of classical information that needs to be exchanged for the conversion. In this pa... View full abstract»

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  • Abelian permutation group problems and logspace counting classes

    Publication Year: 2004 , Page(s): 204 - 214
    Request Permissions | Click to expandAbstract | PDF file iconPDF (388 KB) |  | HTML iconHTML  

    The goal of this paper is to classify abelian permutation group problems using logspace counting classes. Building on McKenzie and Cook's [MC87] classification of permutation group problems into four NC Turing-equivalent sets, we show that all these problems are essentially captured by the generalized logspace mod-class ModL, where ModL is the logspace analogue of ModP (defined by Kobler and Toda ... View full abstract»

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  • Limitations of quantum advice and one-way communication

    Publication Year: 2004 , Page(s): 320 - 332
    Cited by:  Papers (6)
    Request Permissions | Click to expandAbstract | PDF file iconPDF (468 KB) |  | HTML iconHTML  

    Although a quantum state requires exponentially many classical bits to describe, the laws of quantum mechanics impose severe restrictions on how that state can be accessed. This paper shows in three settings that quantum messages have only limited advantages over classical ones. First, we show that BQP/qpoly ⊆ PP/poly, where BQP/qpoly is the class of problems solvable in quantum polynomial ti... View full abstract»

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  • Small spans in scaled dimension

    Publication Year: 2004 , Page(s): 104 - 112
    Request Permissions | Click to expandAbstract | PDF file iconPDF (332 KB) |  | HTML iconHTML  

    Juedes and Lutz (1995) proved a small span theorem for polynomial-time many-one reductions in exponential time. This result says that for language A decidable in exponential time, either the class of languages reducible to A (the lower span) or the class of problems to which A can be reduced (the upper span) is small in the sense of resource-bounded measure and, in particular, that the degree of A... View full abstract»

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  • Parameterized complexity of constraint satisfaction problems

    Publication Year: 2004 , Page(s): 139 - 149
    Request Permissions | Click to expandAbstract | PDF file iconPDF (373 KB) |  | HTML iconHTML  

    We prove a parameterized analog of Schaefer's Dichotomy Theorem: we show that for every finite Boolean constraint family F, deciding whether a formula containing constraints from F has a satisfying assignment of weight exactly k is either fixed-parameter tractable (TPT,) or W[l]-complete. We give a simple characterization of those constraints that make the problem fixed-parameter tractable. The sp... View full abstract»

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  • Dimension, entropy rates, and compression

    Publication Year: 2004 , Page(s): 174 - 183
    Request Permissions | Click to expandAbstract | PDF file iconPDF (351 KB) |  | HTML iconHTML  

    This paper develops relationships between resource-bounded dimension, entropy rates, and compression. New tools for calculating dimensions are given and used to improve previous results about circuit-size complexity classes. Approximate counting of SpanP functions is used to prove that the NP-entropy rate is an upper bound for dimension in Δ3E, the third level of the ex... View full abstract»

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  • Relativized NP search problems and propositional proof systems

    Publication Year: 2004 , Page(s): 54 - 67
    Request Permissions | Click to expandAbstract | PDF file iconPDF (509 KB) |  | HTML iconHTML  

    An NP search problem is the problem of finding a witness to a given NP predicate, and TFNP is the class of total NP search problems. TFNP contains a number of subclasses containing natural problems; for example, PLS is the class of efficient local search heuristics. These classes are characterized by the combinatorial principle that guarantees the existence of a solution; for example, PLS is the c... View full abstract»

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  • The complexity of the covering radius problem on lattices and codes

    Publication Year: 2004 , Page(s): 161 - 173
    Cited by:  Papers (2)
    Request Permissions | Click to expandAbstract | PDF file iconPDF (410 KB) |  | HTML iconHTML  

    We initiate the study of the computational complexity of the covering radius problem for point lattices, and approximation versions of the problem for both lattices and linear codes. We also investigate the computational complexity of the shortest linearly independent vectors problem, and its relation to the covering radius problem for lattices. For the covering radius on n-dimensional lattices, w... View full abstract»

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