2,273 research outputs found
Linear Programming Relaxations for Goldreich's Generators over Non-Binary Alphabets
Goldreich suggested candidates of one-way functions and pseudorandom
generators included in . It is known that randomly generated
Goldreich's generator using -wise independent predicates with input
variables and output variables is not pseudorandom generator with
high probability for sufficiently large constant . Most of the previous
works assume that the alphabet is binary and use techniques available only for
the binary alphabet. In this paper, we deal with non-binary generalization of
Goldreich's generator and derives the tight threshold for linear programming
relaxation attack using local marginal polytope for randomly generated
Goldreich's generators. We assume that input
variables are known. In that case, we show that when , there is an
exact threshold
such
that for , the LP relaxation can determine
linearly many input variables of Goldreich's generator if
, and that the LP relaxation cannot determine
input variables of Goldreich's generator if
. This paper uses characterization of LP solutions by
combinatorial structures called stopping sets on a bipartite graph, which is
related to a simple algorithm called peeling algorithm.Comment: 14 pages, 1 figur
Average-case analysis for the MAX-2SAT problem
AbstractWe propose a simple probability model for MAX-2SAT instances for discussing the average-case complexity of the MAX-2SAT problem. Our model is a “planted solution model”, where each instance is generated randomly from a target solution. We show that for a large range of parameters, the planted solution (more precisely, one of the planted solution pairs) is the optimal solution for the generated instance with high probability. We then give a simple linear-time algorithm based on a message passing method, and we prove that it solves the MAX-2SAT problem with high probability for random MAX-2SAT instances under this planted solution model for probability parameters within a certain range
Spacer Thickness Dependence of Photoluminescence and Raman Scattering Spectra in Au/Spacer/CdSe-Nanoparticle Multilayers
AbstractWe report photoluminescence (PL) and Raman scattering (RS) spectra in Au/spacer/CdSe-nanoparticle multilayers as a function of the distance between the Au film and the CdSe-nanoparticle monolayer. Both the PL and RS intensities were enhanced when the Au-CdSe distance was large and decreased with a decrease in distance. The influence of the localized surface plasmons on the optical properties of the CdSe nanoparticles is discussed. PACS: 78.67.Bf; 78.30.Fs; 78.55.E
- …