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On Defining Integers And Proving Arithmetic Circuit Lower Bounds 总被引:1,自引:1,他引:0
Peter Bürgisser 《Computational Complexity》2009,18(1):81-103
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The Sum of D Small-Bias Generators Fools Polynomials of Degree D 总被引:1,自引:1,他引:0
Emanuele Viola 《Computational Complexity》2009,18(2):209-217
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Emanuele Viola 《Computational Complexity》2005,13(3-4):147-188
We study the complexity of constructing pseudorandom generators (PRGs) from hard functions, focussing on constant-depth circuits. We show that, starting from a function
computable in alternating time O(l) with O(1) alternations that is hard on average (i.e. there is a constant
such that every circuit of size
fails to compute f on at least a 1/poly(l) fraction of inputs) we can construct a
computable by DLOGTIME-uniform constant-depth circuits of size polynomial in n. Such a PRG implies
under DLOGTIME-uniformity. On the negative side, we prove that starting from a worst-case hard function
(i.e. there is a constant
such that every circuit of size
fails to compute f on some input) for every positive constant
there is no black-box construction of a
computable by constant-depth circuits of size polynomial in n. We also study worst-case hardness amplification, which is the related problem of producing an average-case hard function starting from a worst-case hard one. In particular, we deduce that there is no blackbox worst-case hardness amplification within the polynomial time hierarchy. These negative results are obtained by showing that polynomialsize constant-depth circuits cannot compute good extractors and listdecodable codes. 相似文献
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R. F. Streater 《Open Systems & Information Dynamics》2004,11(4):359-375
Let H0 be a selfadjoint operator such that Tr
is of trace class for some
, and let
denote the set of ε-bounded forms, i.e.,
for some
0 $$" align="middle" border="0">
. Let χ := Span
. Let
denote the underlying set of the quantum information manifold of states of the form
. We show that if Tr
,
Presented at the 36th Symposium on Mathematical Physics, ‘Open Systems & Quantum Information’, Toruń, Poland, June 9-12, 2004. 相似文献
1. | the map Φ,
| |
2. | The Orlicz space defined by Φ is the tangent space of at ρ0; its affine structure is defined by the (+1)-connection of Amari | |
3. | The subset of a ‘hood of ρ0, consisting of p-nearby states (those obeying for some 1$$" align="middle" border="0"> ) admits a flat affine connection known as the (-1) connection, and the span of this set is part of the cotangent space of | |
4. | These dual structures extend to the completions in the Luxemburg norms. |
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Agent Communication Languages (ACLs) have been developed to provide a way for agents to communicate with each other supporting
cooperation in Multi-Agent Systems (MAS). In the past few years many ACLs have been proposed for MAS and new standards are
emerging such as the ACL developed by the Foundation for Intelligent Physical Agents (FIPA). Despite these efforts, an important
issue in the research on ACLs is still open and concerns how these languages should deal with failures of agents in asynchronous MAS. The Fault Tolerant Agent Communication Language (
-
) presented in this paper addresses this issue dealing with crash failures of agents.
-
provides high-level communication primitives which support a fault-tolerant anonymous interaction protocol designed for open
MAS. We present a formal semantics for
-
and a formal specification of the underlying agent architecture. This formal framework allows us to prove that the ACL satisfies
a set of well defined knowledge-level programming requirements. To illustrate the language features we show how
-
can be effectively used to write high-level executable specifications of fault tolerant protocols, such as the Contract Net
one. 相似文献
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Remco Duits Michael Felsberg Gösta Granlund Bart ter Haar Romeny 《International Journal of Computer Vision》2007,72(1):79-102
Inspired by the early visual system of many mammalians we consider the construction of-and reconstruction from- an orientation
score
as a local orientation representation of an image,
. The mapping
is a wavelet transform
corresponding to a reducible representation of the Euclidean motion group onto
and oriented wavelet
. This wavelet transform is a special case of a recently developed generalization of the standard wavelet theory and has the
practical advantage over the usual wavelet approaches in image analysis (constructed by irreducible representations of the
similitude group) that it allows a stable reconstruction from one (single scale) orientation score. Since our wavelet transform
is a unitary mapping with stable inverse, we directly relate operations on orientation scores to operations on images in a
robust manner.
Furthermore, by geometrical examination of the Euclidean motion group
, which is the domain of our orientation scores, we deduce that an operator Φ on orientation scores must be left invariant
to ensure that the corresponding operator
on images is Euclidean invariant. As an example we consider all linear second order left invariant evolutions on orientation
scores corresponding to stochastic processes on G. As an application we detect elongated structures in (medical) images and automatically close the gaps between them.
Finally, we consider robust orientation estimates by means of channel representations, where we combine robust orientation
estimation and learning of wavelets resulting in an auto-associative processing of orientation features. Here linear averaging
of the channel representation is equivalent to robust orientation estimation and an adaptation of the wavelet to the statistics
of the considered image class leads to an auto-associative behavior of the system.
The Netherlands Organization for Scientific Research is gratefully acknowledged for financial support. This work has been
supported by EC Grant IST-2003-004176 COSPAL. 相似文献
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Eric Allender Anna Bernasconi Carsten Damm Joachim von zur Gathen Michael Saks Igor Shparlinski 《Computational Complexity》2003,12(1-2):23-47
We study various combinatorial complexity measures of
Boolean functions related to some natural arithmetic problems about
binary polynomials, that is, polynomials over
.
In particular, we consider
the Boolean function deciding whether a given polynomial over
is squarefree. We obtain an exponential lower bound on the size of a
decision tree for this function, and derive an asymptotic formula, having
a linear main term, for its average sensitivity. This allows us to estimate
other complexity characteristics such as the formula size, the average decision
tree depth and the degrees of exact and approximative polynomial
representations of this function. Finally, using a different method, we
show that testing squarefreeness and irreducibility of polynomials over
cannot be done in
for any odd prime p. Similar results are
obtained for deciding coprimality of two polynomials over
as well. 相似文献
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Every Linear Threshold Function has a Low-Weight Approximator 总被引:1,自引:1,他引:0
Rocco A. Servedio 《Computational Complexity》2007,16(2):180-209
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We present new baby steps/giant steps algorithms of asymptotically fast running time for dense matrix problems. Our algorithms compute the determinant, characteristic polynomial, Frobenius normal form and Smith normal form of a dense n × n matrix A with integer entries in
and
bit operations; here
denotes the largest entry in absolute value and the exponent adjustment by +o(1) captures additional factors
for positive real constants C1, C2, C3. The bit complexity
results from using the classical cubic matrix multiplication algorithm. Our algorithms are randomized, and we can certify that the output is the determinant of A in a Las Vegas fashion. The second category of problems deals with the setting where the matrix A has elements from an abstract commutative ring, that is, when no divisions in the domain of entries are possible. We present algorithms that deterministically compute the determinant, characteristic polynomial and adjoint of A with n3.2+o(1) and O(n2.697263) ring additions, subtractions and multiplications.To B. David Saunders on the occasion of his 60th birthday 相似文献
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Hierarchical matrices (
-matrices) approximate matrices in a data-sparse way, and the approximate arithmetic for
-matrices is almost optimal. In this paper we present an algebraic approach for constructing
-matrices which combines multilevel clustering methods with
-matrix arithmetic to compute the
-inverse,
-LU, and the
-Cholesky factors of a matrix. Then the
-inverse,
-LU or
-Cholesky factors can be used as preconditioners in iterative methods to solve systems of linear equations. The numerical
results show that this method is efficient and greatly speeds up convergence compared to other approaches, such as JOR or
AMG, for solving some large, sparse linear systems, and is comparable to other
-matrix constructions based on Nested Dissection. 相似文献
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Pascal Koiran 《Computational Complexity》2005,13(3-4):131-146
Let (n) be the minimum number of arithmetic operations required to build the integer
from the constants 1 and 2. A sequence xn is said to be easy to compute if there exists a polynomial p such that
for all It is natural to conjecture that sequences such as
or n! are not easy to compute. In this paper we show that a proof of this conjecture for the first sequence would imply a superpolynomial lower bound for the arithmetic circuit size of the permanent polynomial. For the second sequence, a proof would imply a superpolynomial lower bound for the permanent or P PSPACE. 相似文献
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Kiran S. Kedlaya 《Computational Complexity》2006,15(1):1-19
We exhibit a quantum algorithm for determining the zeta function of a genus g curve over a finite field
, which is polynomial in g and log(q). This amounts to giving an algorithm to produce provably random elements of the class group of a curve, plus a recipe for
recovering a Weil polynomial from enough of its cyclic resultants. The latter effectivizes a result of Fried in a restricted
setting. 相似文献
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