18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings.

7-10 July 2003

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  • Proceedings 18th IEEE Annual Conference on Computational Complexity

    Publication Year: 2003
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  • Extremal properties of polynomial threshold functions

    Publication Year: 2003, Page(s):3 - 12
    Cited by:  Papers (6)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (370 KB) | HTML iconHTML

    We give new extremal bounds on polynomial threshold function (PTF) representations of Boolean functions. Our results include the following: 1) Almost every Boolean function has PTF degree at most n/2+O(/spl radic/(n log n)). Together with results of Anthony and Alon, we establish a conjecture of Wang and Williams [1991] and Aspnes, Beigel, Furst, and Rudich [1994] up to lower order terms. 2) Every... View full abstract»

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  • Bounded nondeterminism and alternation in parameterized complexity theory

    Publication Year: 2003, Page(s):13 - 29
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (712 KB) | HTML iconHTML

    We give machine characterisations and logical descriptions of a number of parameterized complexity classes. The focus of our attention is the class W[P], which we characterise as the class of all parameterized problems decidable by a nondeterministic fixed-parameter tractable algorithm, whose use of nondeterminism is bounded in terms of the parameter. We give similar characterisations for AW[P], t... View full abstract»

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  • Uniform hardness vs. randomness tradeoffs for Arthur-Merlin games

    Publication Year: 2003, Page(s):33 - 47
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1360 KB) | HTML iconHTML

    Impagliazzo and Wigderson proved a uniform hardness vs. randomness "gap result" for BPP. We show an analogous result for AM: Either Arthur-Merlin protocols are very strong and everything in E=DTIME(2/sup O(n)/) can be proved to a subexponential time verifier, or else Arthur-Merlin protocols are weak and every language in AM has a polynomial time nondeterministic algorithm in the uniform average-ca... View full abstract»

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  • A zero one law for RP

    Publication Year: 2003, Page(s):48 - 52
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (389 KB) | HTML iconHTML

    We show that if RP has p-measure nonzero then ZPP=EXP. As corollaries, we obtain a zero-one law for RP, and that both probabilistic classes ZPP and RP have the same p-measure. Finally we prove that if NP has p-measure nonzero then NP=AM. View full abstract»

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  • Hardness vs. randomness within alternating time

    Publication Year: 2003, Page(s):53 - 69
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (462 KB) | HTML iconHTML

    We study the complexity of building pseudorandom generators (PRGs) with logarithmic seed length from hard functions. We show that, starting from a function f:{0,1}/sup l//spl rarr/{0,1} that is mildly hard on average, i.e. every circuit of size 2/sup /spl Omega/(l)/ fails to compute f on at least a 1/poly(l) fraction of inputs, we can build a PRG: {0,1}/sup O(logn)//spl rarr/{0,1}/sup n/ computabl... View full abstract»

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  • Lower bounds for predecessor searching in the cell probe model

    Publication Year: 2003, Page(s):73 - 83
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (538 KB) | HTML iconHTML

    We consider a fundamental problem in data structures, static predecessor searching: Given a subset S of size n from the universe [m], store S so that queries of the form "What is the predecessor of x in S?" can be answered efficiently. We study this problem in the cell probe model introduced by Yao [1981]. Recently, Beame and Fich [2002] obtained optimal bounds on the number of probes needed by an... View full abstract»

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  • Minimization of decision trees is hard to approximate

    Publication Year: 2003, Page(s):84 - 92
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (501 KB) | HTML iconHTML

    Decision trees are representations of discrete functions with widespread applications in, e.g., complexity theory and data mining and exploration. In these areas it is important to obtain decision trees of small size. The minimization problem for decision trees is known to be NP-hard. The problem is even hard to approximate up to any constant factor. View full abstract»

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  • Optimal separation of EROW and CROW PRAMs

    Publication Year: 2003, Page(s):93 - 104
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (370 KB) | HTML iconHTML

    We consider the problem of evaluating a Boolean function on PRAMs. We exhibit a Boolean function f:{0,1}/sup n//spl rarr/{0,1} that can be evaluated in time O(log log n) in a deterministic CROW (concurrent read owner write) PRAM model, but requires time /spl Omega/(log n) in EROW (exclusive read owner write) PRAM. Our lower bound also holds in the randomized Monte Carlo EROW model. This Boolean fu... View full abstract»

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  • Near-optimal lower bounds on the multi-party communication complexity of set disjointness

    Publication Year: 2003, Page(s):107 - 117
    Cited by:  Papers (36)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (564 KB) | HTML iconHTML

    We study the communication complexity of the set disjointness problem in the general multiparty model. For t players, each holding a subset of a universe of size n, we establish a near-optimal lower bound of /spl Omega/(n/(t log t)) on the communication complexity of the problem of determining whether their sets are disjoint. In the more restrictive one-way communication model, in which the player... View full abstract»

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  • Rectangle size bounds and threshold covers in communication complexity

    Publication Year: 2003, Page(s):118 - 134
    Cited by:  Papers (14)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (449 KB) | HTML iconHTML

    We investigate the power of the most important lower bound technique in randomized communication complexity, which is based on an evaluation of the maximal size of approximately monochromatic rectangles, with respect to arbitrary distributions on the inputs. While it is known that the 0-error version of this bound is polynomially tight for deterministic communication, nothing in this direction is ... View full abstract»

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  • The complexity of unique k-SAT: an isolation lemma for k-CNFs

    Publication Year: 2003, Page(s):135 - 141
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (453 KB) | HTML iconHTML

    We provide some evidence that unique k-SAT is as hard to solve as general k-SAT, where k-SAT denotes the satisfiability problem for k-CNFs and unique k-SAT is the promise version where the given formula has 0 or 1 solutions. Namely, defining for each k/spl ges/1, s/sub k/=inf{/spl delta//spl ges/0|/spl exist/aO(2/sup /spl delta/n/)-time randomized algorithm for k-SAT} and, similarly, /spl sigma//s... View full abstract»

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  • Parameterized complexity for the skeptic

    Publication Year: 2003, Page(s):147 - 168
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (726 KB) | HTML iconHTML

    The goal is to provide a tourist guide, with an eye towards structural issues, to what I consider some of the major highlights of parameterized complexity. View full abstract»

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  • Quantum certificate complexity

    Publication Year: 2003, Page(s):171 - 178
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (524 KB) | HTML iconHTML

    Given a Boolean function f, we study two natural generalizations of the certificate complexity C(f): the randomized certificate complexity RC(f) and the quantum certificate complexity QC(f). Using Ambainis' adversary method, we exactly characterize QC(f) as the square root of RC(f). We then use this result to prove the new relation R/sub 0/(f)=O(Q/sub 2/(f)/sup 2/Q/sub 0/(f)log n) for total f, whe... View full abstract»

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  • Quantum query complexity and semi-definite programming

    Publication Year: 2003, Page(s):179 - 193
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (426 KB) | HTML iconHTML

    We reformulate quantum query complexity in terms of inequalities and equations for a set of positive semidefinite matrices. Using the new formulation we: 1) show that the workspace of a quantum computer can be limited to at most n+k qubits (where n and k are the number of input and output bits respectively) without reducing the computational power of the model; 2) give an algorithm that on input t... View full abstract»

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  • On statistical query sampling and NMR quantum computing

    Publication Year: 2003, Page(s):194 - 205
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (614 KB) | HTML iconHTML

    We introduce a "statistical query sampling" model, in which the goal of an algorithm is to produce an element in a hidden set S/spl sube/{0,1}/sup n/ with reasonable probability. The algorithm gains information about S through oracle calls (statistical queries), where the algorithm submits a query function g(/spl middot/) and receives an approximation to Pr/sub x/spl isin/S/[g(x)=1]. We show how t... View full abstract»

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  • Derandomization and distinguishing complexity

    Publication Year: 2003, Page(s):209 - 220
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (616 KB) | HTML iconHTML

    We continue an investigation of resource-bounded Kolmogorov complexity and derandomization techniques begun in [E. Allender (2001), E. Allender et al., (2002)]. We introduce nondeterministic time-bounded Kolmogorov complexity measures (KNt and KNT) and examine the properties of these measures using constructions of hitting set generators for nondeterministic circuits [P. B. Miltersen et al., (1999... View full abstract»

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  • Extracting the mutual information for a triple of binary strings

    Publication Year: 2003, Page(s):221 - 229
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (482 KB) | HTML iconHTML

    We say that the mutual information of a triple of binary strings a, b, c can be extracted if there exists a string d such that a, b, and c are independent given d, and d is simple conditional to each of the strings a, b, c. This is an analog of the well-known Gacs-Korner (1973) definition of extrability of the mutual information for a pair of binary strings. We prove that (in contrast to the case ... View full abstract»

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  • The complexity of stochastic sequences

    Publication Year: 2003, Page(s):230 - 235
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (346 KB) | HTML iconHTML

    We observe that known results on the Kolmogorov complexity of prefixes of effectively stochastic sequences extend to corresponding random sequences. First, there are recursively random sequences such that for any nondecreasing and unbounded computable function f and for almost all n, the uniform complexity of the length n prefix of the sequence is bounded by f(n). Second, a similar result with bou... View full abstract»

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  • A combinatorial characterization of resolution width

    Publication Year: 2003, Page(s):239 - 247
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (386 KB) | HTML iconHTML

    We provide a characterization of the resolution width introduced in the context of propositional proof complexity in terms of the existential pebble game introduced in the context of finite model theory. The characterization is tight and purely combinatorial. Our first application of this result is a surprising proof that the minimum space of refuting a 3-CNF formula is always bounded from below b... View full abstract»

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  • Memoization and DPLL: formula caching proof systems

    Publication Year: 2003, Page(s):248 - 259
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (585 KB) | HTML iconHTML

    A fruitful connection between algorithm design and proof complexity is the formalization of the DPLL approach to satisfiability testing in terms of tree-like resolution proofs. We consider extensions of the DPLL approach that add some version of memoization, remembering formulas the algorithm has previously shown unsatisfiable. Various versions of such formula caching algorithms have been suggeste... View full abstract»

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  • Inapproximability - some history and some open problems

    Publication Year: 2003, Page(s):265 - 266
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (225 KB) | HTML iconHTML

    The purpose of this talk is to give an overview of the status of some problems in approximability. View full abstract»

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  • Holographic proofs and derandomization

    Publication Year: 2003, Page(s):269 - 283
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (755 KB) | HTML iconHTML

    We derive a stronger consequence of EXP having polynomial-size circuits than was known previously, namely that there is a simulation of P in MAPOLYLOG that fools all deterministic polynomial-time adversaries. Using the connection between circuit lower bounds and derandomization, we obtain uniform assumptions for derandomizing BPP. Our results strengthen the space-randomness tradeoffs of Sipser, Ni... View full abstract»

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  • Three-query PCPs with perfect completeness over non-Boolean domains

    Publication Year: 2003, Page(s):284 - 299
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (408 KB) | HTML iconHTML

    We study nonBoolean PCPs that have perfect completeness and read three positions from the proof. For the case when the proof consists of values from a domain of size d for some integer constant d/spl ges/2, we construct a nonadaptive PCP with perfect completeness and soundness d/sup -1/+d/sup -2/+/spl epsiv/, for any constant /spl epsiv/>0, and an adaptive PCP with perfect completeness and soun... View full abstract»

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  • List decoding with side information

    Publication Year: 2003, Page(s):300 - 309
    Cited by:  Papers (14)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (593 KB) | HTML iconHTML

    Under list decoding of error-correcting codes, the decoding algorithm is allowed to output a small list of codewords that are close to the noisy received word. This relaxation permits recovery even under very high noise thresholds. We consider one possible scenario that would permit disambiguating between the elements of the list, namely where the sender of the message provides some hopefully smal... View full abstract»

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