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A probabilistic algorithm for determining the minimum weight of cyclic codes

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 1998年第10期E81A卷 2170-2173页

作者： Mohri, M Morii, M Kagawa Jr Coll Dept Management & Informat Proc Kagawa 7690201 Japan Univ Tokushima Fac Engn Dept Informat Sci & Intelligent Syst Tokushima 7708506 Japan

A method is presented for determining the minimum weight of cyclic codes. It is a probabilistic algorithm. This algorithm is used to find, the minimum weight of codes far too large to be treated by any known algorithm. It is based on a probabilistic algorithm for determining the minimum weight of linear code by Jeffrey S. Leon. By using this method, the minimum weight of cyclic codes is computed efficiently.

关键词： minimum weight cyclic codes probabilistic algorithm

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A probabilistic algorithm FOR VERIFYING MATRIX PRODUCTS USING O(N(2)) TIME AND LOG(2)N+O(1) RANDOM BITS

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INFORMATION PROCESSING LETTERS 1993年第2期45卷 107-110页

作者： KIMBREL, T SINHA, RK UNIV WASHINGTON DEPT COMP SCI & ENGNFR-35SEATTLEWA 98195

Given two n × n matrices A and B, computing their product is a classic problem. We consider a related decision problem: given three n × n matrices A, B, and C, how difficult is it to verify whether AB = C? A method similar to Freivalds' probabilistic algorithm is used here. Our method is also similar to the constructions of Alon et al., particularly their powering construction. The constructions of Alon et al. can be used to implement Freivalds' algorithm. While Naor and Naor and Alon et al. have solved a more general problem, our algorithm yields a slightly better constant (in terms of the random bit requirement) in the general case. More importantly, our algorithm is much simpler and more direct, and it can easily be extended to make the probability of error less than any Ε with only [log2(1/Ε)] additional random bits. In Section 2, we present the simplest version of the algorithm for integer matrices. Section 3 shows how to improve the bit complexity, Section 4 extends the algorithm to matrices over finite fields, and Section 5 shows how to reduce the error probability.

关键词： probabilistic algorithm DESIGN OF algorithmS

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probabilistic algorithm for Determining Bit Multipliers in the Problem of Factoring Integers

Probabilistic Algorithm for Determining Bit Multipliers in t...

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International Siberian Conference on Control and Communications (SIBCON)

作者： Ogorodnikov, Y. Y. Omsk State Tech Univ OmSTU Complex Protect Informat Dept Omsk Russia

ISBN: (纸本)9781479971039

The paper presents a probabilistic algorithm for determining the bit multipliers in the problem of factoring integers, the most famous application of which is the use of the algorithm RSA. An algorithm is based on the reduction of factorization problem to the problem of satisfiability of Boolean formulas, that is, in turn, reduce to continuous real functional. The obtained functional is minimized by method of simple iterations and the results are projected from real variables to Boolean with using Bayesian approach. The numerical experiments were performed and the variants of further application are proposed. An important advantage of the developed method is the polynomial time of calculating.

关键词： factoring satisfiability of Boolean formulas (SAT) method of simple iteration projection real variables to Boolean Bayesian approach probabilistic algorithm

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Simulation of powder transport in plasma jet via hybrid Lattice Boltzmann method and probabilistic algorithm

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SURFACE & COATINGS TECHNOLOGY 2006年第3-4期201卷 886-894页

作者： Zhang, Haiou Hu, Shengde Wang, Guilan Huazhong Univ Sci & Technol State Key Lab Plast Forming Simulat & Die & Mold Wuhan 430074 Peoples R China

When plasma is used to spray coatings on a mould surface, the states of the plasma jet and powder particles have great influence on the quality of the spray layer. In order to find a simple and efficient simulation for the states of the plasma jet and powder particles, an attempt of modeling was made by hexagonal 7-bit Lattice Boltzmann method (LBM) and a probabilistic algorithm in this paper. The velocity and temperature field of the plasma jet and particles are calculated and compared with those obtained by previous models and measurements. The dynamic moving process, accelerating course, maximal speed and distribution of powder particles are calculated by the present model. The optimal spraying distance and deposition efficiency under different spraying conditions are also acquired. It can be concluded that the combined model is competent for numerical simulation of the atmospheric plasma spraying. Simulation by LBM is simpler and faster than that by traditional methods. LBM is also a computational method that offers flexibility and outstanding capacity of parallel computation. (c) 2006 Elsevier B.V. All rights reserved.

关键词： plasma spray simulation and modeling Lattice Boltzmann method probabilistic algorithm

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A probabilistic algorithm for verifying polynomial middle product in linear time

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INFORMATION PROCESSING LETTERS 2018年 139卷 30-34页

作者： Giorgi, Pascal Univ Montpellier LIRMM CNRS Montpellier France

Polynomial multiplication and its variants are a key ingredient in effective computer algebra. While verifying a polynomial product is a well known task, it was not yet clear how to do a similar approach for its middle product variant. In this short note, we present a new algorithm that provides such a verification with the same complexity and probability that for the classical polynomial multiplication. Furthermore, we extend our algorithm to verify any operations that compute only a certain chunk of the product, which is the case for instance of the well known short product operation. (C) 2018 Elsevier B.V. All rights reserved.

关键词： probabilistic algorithm Design of algorithm Computation on polynomials Polynomial multiplication

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A probabilistic algorithm FOR VERTEX CONNECTIVITY OF GRAPHS

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INFORMATION PROCESSING LETTERS 1982年第3期15卷 135-136页

作者： BECKER, M DEGENHARDT, W DOENHARDT, J HERTEL, S KANINKE, G KEBER, W MEHLHORN, K NAHER, S ROHNERT, H WINTER, T Fachbereich 10 Angewandte Mathematik und Informatik Universität des Saarlandes D-6600 Saarbrücken Fed. Rep. Germany

This review presents a probabilistic algorithm which computes the vertex connectivity of an undirected graph G=(V,E) in expected time Omicron ((-log epsilon) times the absolute value of V to the 31/2 power times the absolute value of E) with error probability at most epsilon provided that the absolute value of E is less than or equal to 11/2d times the absolute value of V squared for some universal constant d less than 1.

关键词： probabilistic algorithm sparse graphs vertex connectivity network flow complexity

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A probabilistic algorithm for Calculating Similarities

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AUTOMATIC DOCUMENTATION AND MATHEMATICAL LINGUISTICS 2019年第5期53卷 234-236页

作者： Vinogradov, D. V. Russian Acad Sci Fed Res Ctr Comp Sci & Control Moscow 119333 Russia Russian State Univ Humanities Moscow 125993 Russia

In this paper, we describe a new probabilistic algorithm for calculating hypotheses as the results of similarities between training examples for a machine learning problem based on a binary similarity operation. Unlike previously proposed probabilistic algorithms, the order of accounting for training examples is fixed for all hypotheses. This algorithm is useful for implementation using a GPGPU. The main result of this paper is the independence of the order of the appearance of training examples of the probabilities of each similarity in the sample.

关键词： similarity probabilistic algorithm counter-example

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Non-Contact Guided Waves Tomographic Imaging of Plate-Like Structures Using a probabilistic algorithm

Non-Contact Guided Waves Tomographic Imaging of Plate-Like S...

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13th Asia-Pacific Conference on Non-Destructive Testing (APCNDT)

作者： Albiruni, Farabirazy Cho, Younho Lee, Joon-Hyun Ahn, Bong-Young Pusan Natl Univ Sch Mech Engn Pusan 607735 South Korea Korea Inst Energy Technol Evaluat & Planning Seoul 135280 South Korea Korea Inst Stand & Sci Taejon 305340 South Korea

A non-contact testing with laser generated ultrasonic transmitter and an air-coupled transducer is very attractive technique in guided wave inspection. It can be used for online inspection and structural health monitoring (SHM) where contact method with embedded sparse sensors can not be applied such as the case of high temperature application. In this paper, tomography based on probabilistic algorithm was employed in conjunction with the hybrid non-contact method. This present approach can be successfully used for detecting, locating and imaging multi-defect in plates. This algorithm is based on the use of signal difference coefficient of guided waves acquired for good and faulty conditions. The simplicity of this algorithm makes it suitable to be implemented to non-contact based online inspection scheme. [doi:10.2320/matertrans.I-M2011853]

关键词： hybrid non-contact ultrasonic guided wave tomography plate-like structures probabilistic algorithm

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A Reliability-Based Computation Method for the Weight Distribution of LDPC Codes Using the probabilistic algorithm

A Reliability-Based Computation Method for the Weight Distri...

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IEEE International Symposium on Information Theory (ISIT)

作者： Hirotomo, Masanori Mohri, Masami Morii, Masakatu Kobe Univ Grad Sch Engn Kobe Hyogo 6578501 Japan Gifu Univ Informat & Multimedia Ctr Gifu 501-1193 Japan

ISBN: (纸本)9781457705953

In the analysis of maximum-likelihood decoding performance of low-density parity-check (LDPC) codes, the weight distribution is an important factor. Some methods based on the error impluse method have presented in order to estimate the weight distribution of LDPC codes. However, these methods have no scheme which determine the number of codeword in LDPC codes. In this paper, we propose a reliability-based computation method for the weight distribution of LDPC codes using the probabilistic algorithm. Using the proposed method, we can determine the weight distribution of LDPC codes with small failure probability.

关键词： Approximation algorithms LDPC codes Linear code Maximum likelihood decoding Parity check codes probabilistic logic Reliability Vectors error impluse method failure probability low density parity check codes maximum likelihood decoding maximum-likelihood decoding performance parity check codes probabilistic algorithm probability reliability reliability-based computation method weight distribution

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A probabilistic algorithm for Verification of Geometric Theorems 1

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13th International Conference on algorithmic Aspects in Information and Management (AAIM)

作者： Chen, Mingyan Zeng, Zhenbing Shanghai Univ Dept Math Shanghai 200444 Peoples R China

ISBN: (数字)9783030271954

ISBN: (纸本)9783030271954;9783030271947

In this paper we combine the Schwartz-Zippel theorem with statistical inference theory and develop a new probabilistic algorithm instead of deterministic algorithms for geometry theorem proving. Our work includes an improved algorithm for estimating the upper bounds in the pseudo-remainder, and three selection criteria for statistical populations.

关键词： Geometric theorems proving probabilistic algorithm Selection criterion for statistical population Statistical inference

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