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51
Lower Bounds for the Polynomial Calculus and the Gröbner Basis Algorithm
, 1997
"... this paper, all the lower bounds show that in fact any refutation of some initial polynomials has to contain a polynomial f with large degree of f . ..."
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Cited by 21 (1 self)
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this paper, all the lower bounds show that in fact any refutation of some initial polynomials has to contain a polynomial f with large degree of f .
Width Optimality Results for Resolution and Degree Lower Bounds for Polynomial Calculus
, 2000
"... This paper is concerned with the complexity of proofs and of searching for proofs in two propositional proof systems: Resolution and Polynomial Calculus (PC). First we show that the recently proposed algorithm of BenSasson and Wigderson [2] for searching for proofs in resolution cannot give better t ..."
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This paper is concerned with the complexity of proofs and of searching for proofs in two propositional proof systems: Resolution and Polynomial Calculus (PC). First we show that the recently proposed algorithm of BenSasson and Wigderson [2] for searching for proofs in resolution cannot give better
The index calculus method using nonsmooth polynomials
 Mathematics of Computation
, 2001
"... Abstract. We study a generalized version of the index calculus method for the discrete logarithm problem in Fq, whenq = p n, p is a small prime and n →∞. The database consists of the logarithms of all irreducible polynomials of degree between given bounds; the original version of the algorithm uses ..."
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Cited by 6 (2 self)
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Abstract. We study a generalized version of the index calculus method for the discrete logarithm problem in Fq, whenq = p n, p is a small prime and n →∞. The database consists of the logarithms of all irreducible polynomials of degree between given bounds; the original version of the algorithm uses
PHASE SPACE ANALYSIS AND FUNCTIONAL CALCULUS FOR THE LINEARIZED LANDAU AND BOLTZMANN OPERATORS
"... doi:10.3934/xx.xx.xx.xx pp. X–XX ..."
Summation polynomial algorithms for elliptic curves in characteristic two
"... Abstract. The paper is about the discrete logarithm problem for elliptic curves over characteristic 2 finite fields F2n of prime degree n. We consider practical issues about index calculus attacks using summation polynomials in this setting. The contributions of the paper include: a choice of variab ..."
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Cited by 4 (0 self)
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Abstract. The paper is about the discrete logarithm problem for elliptic curves over characteristic 2 finite fields F2n of prime degree n. We consider practical issues about index calculus attacks using summation polynomials in this setting. The contributions of the paper include: a choice
Satisfying Subtype Inequalities in Polynomial Space
, 1997
"... This paper studies the complexity of type inference in lambdacalculus with subtyping. Type inference is equivalent to solving systems of subtype inequalities. We consider simple types ordered structurally from an arbitrary set of base subtype assumptions. In this case, we give a PSPACE upper bound. ..."
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Cited by 17 (0 self)
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. Together with the known lower bound, this result settles completely the complexity of type inference over simple types, which is PSPACEcomplete. We use a technique of independent theoretical interest that simplifies existing methods developed in the literature. Finally the algorithm, although mainly
A stochastic modeling methodology based on weighted Wiener chaos and Malliavin calculus,
 Proc. Natl. Acad. Sci. USA
, 2009
"... In many stochastic partial differential equations (SPDEs) involving random coefficients, modeling the randomness by spatial white noise may lead to illposed problems. Here we consider an elliptic problem with spatial Gaussian coefficients and present a methodology that resolves this issue. It is b ..."
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Cited by 6 (2 self)
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(x). This approach is based on Malliavin calculus and Wiener chaos expansion (WCE) with respect to CameronMartin basis (see ref. 9 and next section). The CameronMartin basis consists of random variables ξ α , where α = (α 1 , α 2 , . . .) is a multiindex with nonnegative integer entries (see the next section
What is an Efficient Implementation of the λcalculus?
, 1991
"... We propose to measure the efficiency of any implementation of the λcalculus as a function of a new parameter ν, that is itself a function of any λexpression. Complexity is expressed here as a function of ν just as runtime is expressed as a function of the input size n in ordinary analysis of algori ..."
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Cited by 3 (0 self)
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of algorithms. This enables implementations to be compared for worst case efficiency. We argue that any implementation must have complexity Ω(ν), i.e. a linear lower bound. Furthermore, we show that implementations based upon Turner Combinators or Hughes Supercombinators have complexities 2 Ω(ν), i
DOI: 10.1007/s0052600302104
, 2003
"... Abstract. We give a new proof of regularity of biharmonic maps from fourdimensional domains into spheres, showing first that the biharmonic map system is equivalent to a set of bilinear identities in divergence form. The method of reverse Hölder inequalities is used next to prove continuity of sol ..."
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elliptic equations with critical nonlinearities in lower order derivatives. Mathematics Subject Classification (2000): 35J60, 35H20 1.
Results 1  10
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