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第12届分布式计算及其应用国际学术研讨会

作者： Wenjing LI Shuang LI Zhong-ming Lin Weizhi LIAO College of Computer and Information Engineering Guangxi Teachers Education University College of Mathematics Physics and Information Engineering Jiaxing University

In order to solve the parallel algorithm for Petri nets system with concurrent function, to realize the parallel control and execution of the Petri nets, the Petri nets parallel subnets conditions were proposed, that provides the theory basis for judging P- invariant whether was the parallel subnet. Firstly, we according to the concurrent character of Petri net model, to analyze the parallelism of Petri net system, Pinvariants the solving process and it's subnet division were given;Secondly, the Petri nets parallel subnets conditions were proposed, gives P- invariant constituted of Petri net parallel subnets decision theorem, and the theoretical proof and example verification;Finally, A Petri net parallel subnet division algorithm based on P- invariants were given. Theoretical validate and experimental result shows that Petri nets parallel subnets conditions set and divided algorithm were correct and effective.

关键词： Petri nets P-invariant parallel subnet divided condition division algorithm

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Grobner Bases for Lattices and an Algebraic Decoding algorithm

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IEEE TRANSACTIONS ON COMMUNICATIONS 2013年第4期61卷 1222-1230页

作者： Aliasgari, Malihe Sadeghi, Mohammad-Reza Panario, Daniel Amirkabir Univ Technol Dept Math & Comp Sci Tehran Iran Carleton Univ Sch Math & Stat Ottawa ON K1S 5B6 Canada

In this paper we present Grobner bases for lattices given in a general form, including integer and non-integer lattices. Grobner bases for binary linear codes were introduced by Borges-Quintana et al. [4]. We extend their work to non-binary group block codes. Then, given a lattice Lambda and its associated label code L, which is a group code, we define an ideal for L. A Grobner basis is assigned to Lambda as the Grobner basis of its label code L. Since the associated label code for integer and non-integer lattices are group codes, the assigned Grobner bases can be obtained for both cases. Using this Grobner basis an algebraic decoding algorithm is introduced. We provide an example of the decoding method for a lower dimension lattice. We explain that the complexity of this decoding method depends on the division algorithm and show this decoding method has polynomial time complexity. Experiments for some versions of root lattices (E-7 and E-8) show that for low SNR the performance of these lattices is near to the lower bounds given in [16].

关键词： Grobner bases division algorithm lattices label code

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Quotient Prediction for Low Power division

Quotient Prediction for Low Power Division

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IEEE 26th International System-on-Chip Conference (SOCC)

作者： Krishnamoorthy, Prakash Tekumalla, Ramesh LSI Corp APAC SOC Design Allentown PA 18109 USA LSI Corp APAC SOC Dev Allentown PA 18109 USA

ISBN: (纸本)9781479911660

This work presents a variation of the non restoring division algorithm that has been optimized for low power consumption. The approach uses the value of the partial remainder at any stage in the computation to predict the quotient bits for a certain number of steps thereby allowing an equal number of computation steps to be skipped. This results in a significant reduction in switching activity in the computational stages. Simulations using the novel divider show up to 40% reduction in sequential switching activity and 20% reduction in combinational switching activity. On an average, this method uses 59% less addition operations as compared to the regular non restoring division algorithm.

关键词： division algorithm Quotient Sequential switching arithmetic

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Research on Petri nets parallelization the functional divided conditions

Research on Petri nets parallelization the functional divide...

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12th International Symposium on Distributed Computing and Applications to Business, Engineering and Science (DCABES)

作者： Li, Wenjing Li, Shuang Lin, Zhong-ming Liao, Weizhi Guangxi Teachers Educ Univ Coll Comp & Informat Engn Nanning Peoples R China Jiaxing Univ Coll Math Phys & Inf Eng Jiaxing Peoples R China

ISBN: (纸本)9780769550602

In order to solve the parallel algorithm for Petri nets system with concurrent function, to realize the parallel control and execution of the Petri nets, the Petri nets parallel subnets conditions were proposed, that provides the theory basis for judging P- invariant whether was the parallel subnet. Firstly, we according to the concurrent character of Petri net model, to analyze the parallelism of Petri net system, P-invariants the solving process and it's subnet division were given;Secondly, the Petri nets parallel subnets conditions were proposed, gives P- invariant constituted of Petri net parallel subnets decision theorem, and the theoretical proof and example verification;Finally, A Petri net parallel subnet division algorithm based on P- invariants were given. Theoretical validate and experimental result shows that Petri nets parallel subnets conditions set and divided algorithm were correct and effective.

关键词： Petri nets P-invariant parallel subnet divided condition division algorithm

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An algorithm facilitating Fast BCD division on Low End Processors using Ancient Indian Vedic Mathematics Sutras

An algorithm facilitating Fast BCD Division on Low End Proce...

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International Conference on Communications, Devices and Intelligent Systems (COOlS)

作者： Sengupta, Diganta Sultana, Mahamuda Chaudhuri, Atal Jadavpur Univ Dept Comp Sci & Engn Kolkata 700032 W Bengal India

ISBN: (纸本)9781467346986;9781467346993

The last decade or two has witnessed a rapid evolution of the technological world with the introduction of fast processors loaded with higher amount of cache memories. Accordingly, the system architecture demanded better development to suit the rising demand for the technological advancements. Miniaturizations of components and VLSI integration have given rise to bulk advanced memory chips being grafted on even smaller amount of space thus giving access to higher amount of physical memory within exhaust limits of average applications. But the low end processors having limited memory still crave for fast applications, which are slowly going out of bounds for these devices due to the space and time complexity. The four elementary operations - addition, subtraction, multiplication and division form the basis for any type of application. Out of the four, the latter one, namely division, is a highly expensive and time consuming operation. This paper proposes a fast division algorithm based on Ancient Indian Vedic Mathematics Sutras for low end processors having limited memory. The novelty of the algorithm is that it requires a very small amount of memory for execution but performs the division mechanism much faster than the conventional division algorithms in literature, and is equally suitable for high end processors also. The algorithm has been tested on conventional mid range desktop processors and has furnished results with numbers having number of bits greater than 50 (15 digit numbers), the upper ceiling of computable numbers for conventional algorithms. It has been observed that the Vedic division algorithm can divide numbers having up to 38 digits (127 bits) in the present form, if modified it can divide even bigger numbers.

关键词： Vedic division algorithm division algorithm Fast division algorithm Low End Processors

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Obtaining more Karatsuba-like formulae over the binary field

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IET INFORMATION SECURITY 2012年第1期6卷 14-19页

作者： Fan, H. Gu, M. Sun, J. Lam, K. -Y. Tsinghua Univ Sch Software Tsinghua Natl Lab Informat Sci & Technol Key Lab Informat Syst SecurMinist Educ Beijing 100084 Peoples R China

The aim of this study is to find more Karatsuba-like formulae for a fixed set of moduli polynomials in GF(2)[x]. To this end, a theoretical framework is established. The authors first generalise the division algorithm, and then present a generalised definition of the remainder of integer division. Finally, a generalised Chinese remainder theorem is used to achieve their initial goal. As a by-product of the generalised remainder of integer division, the authors rediscover Montgomery's N-residue and present a systematic interpretation of definitions of Montgomery's multiplication and addition operations.

关键词： Montgomery N-residue Montgomery multiplication generalised Chinese remainder theorem Algebra cryptography moduli polynomials addition operations integer division remainder Data security Cryptography Combinatorial mathematics Karatsuba-like formulae number theory polynomials binary field division algorithm

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Design of High-Speed Iterative Dividers in GF(2^m)

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JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 2011年第3期27卷 953-967页

作者： Shieh, Mng-Der Lin, Wen-Ching Wu, Chien-Ming Natl Cheng Kung Univ Dept Elect Engn Tainan 701 Taiwan Natl Appl Res Labs Chip Implementat Ctr Hsinchu 300 Taiwan

Fast algorithms for high-speed divider design in finite fields GF(2(m)) are very crucial in applications like cryptosystems. In this paper, we reformulated the conventional iterative division algorithm by changing the pre-defined variable and then updating its initial value accordingly. The reformulated division algorithm allows a restructuring of the divider architecture to further improve its operating speed without increasing latency or area cost. Using the proposed fast algorithm, we developed two high-speed iterative dividers based on the semi-systolic and bit-serial systolic architectures. Analytical results show that the cost of the initial value update and variable transformation in the reformulated algorithm is almost negligible in the hardware implementation. Our divider designs improve the critical path delay. Compared with related divider designs, the proposed designs have time and area advantages.

关键词： division algorithm finite field high-speed Stein's algorithm systolic array

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Polynomial asymptotes of the second kind

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INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY 2011年第2期42卷 276-282页

作者： Dobbs, David E. Univ Tennessee Dept Math Knoxville TN 37996 USA

This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and conics. Prerequisites include the division algorithm for polynomials with coefficients in the field of real numbers and elementary facts about limits from calculus. This note could be used as enrichment material in courses ranging from Calculus to Real Analysis to Abstract Algebra.

关键词： asymptotic functions limit polynomial rational function degree division algorithm hyperbola

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An efficient key-lock-pair mechanism based on division algorithm

An efficient key-lock-pair mechanism based on division algor...

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International Conference on Multimedia and Ubiquitous Engineering

作者： Huang, Hui-Feng Chang, Chin-Chen Natl Taichung Inst Technol Dept Informat Management Taichung 404 Taiwan Feng Chia Univ Dept Informat Engn & Comp Taichung 40724 Taiwan

ISBN: (纸本)9780769527772

In the access control of a file system, the Chinese Remainder Theorem (CRT) is a method used to establish the key-lock-pair mechanism, However, the key computed using CRT will take much more time to add up a new file. In order to improve upon this, we show that the key-lock-pair mechanism based on the division algorithm can be extended very efficiently when a file is added to the file system. Also, it can be applied to delete a file or to update the access rights of a file in the file system. Therefore, the proposed method is very useful for the dynamic file system.

关键词： key-lock-pair mechanism Chinese Remainder Theorem division algorithm

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Newton-Raphson algorithms for Floating-Point division Using an FMA

Newton-Raphson Algorithms for Floating-Point Division Using ...

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21st IEEE International Conference on Application-Specific Systems, Architectures and Processors

作者： Louvet, Nicolas Muller, Jean-Michel Panhaleux, Adrien Univ Lyon UCBL INRIA ENS LyonCNRSLIP Lyon France

ISBN: (纸本)9781424469673

Since the introduction of the Fused Multiply and Add (FMA) in the IEEE-754-2008 standard [6] for floating-point arithmetic, division based on Newton-Raphson's iterations becomes a viable alternative to SRT-based divisions. The Newton-Raphson iterations were already used in some architecture prior to the revision of the IEEE-754 norm. For example, Itanium architecture already used this kind of iterations [8]. Unfortunately, the proofs of the correctness of binary algorithms do not extend to the case of decimal floating-point arithmetic. In this paper, we present general methods to prove the correct rounding of division algorithms using Newton-Raphson's iterations in software, for radix 2 and radix 10 floating-point arithmetic.

关键词： floating-point arithmetic decimal floating-point arithmetic division algorithm Newton-Raphson iterations

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