Semirings And Their Applications

Author : Jonathan S. Golan
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 54,5 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9789401593335

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Semirings and their Applications by Jonathan S. Golan Pdf

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world. - Nikolai Ivanovich Lobatchevsky This book is an extensively-revised and expanded version of "The Theory of Semirings, with Applicationsin Mathematics and Theoretical Computer Science" [Golan, 1992], first published by Longman. When that book went out of print, it became clear - in light of the significant advances in semiring theory over the past years and its new important applications in such areas as idempotent analysis and the theory of discrete-event dynamical systems - that a second edition incorporating minor changes would not be sufficient and that a major revision of the book was in order. Therefore, though the structure of the first «dition was preserved, the text was extensively rewritten and substantially expanded. In particular, references to many interesting and applications of semiring theory, developed in the past few years, had to be added. Unfortunately, I find that it is best not to go into these applications in detail, for that would entail long digressions into various domains of pure and applied mathematics which would only detract from the unity of the volume and increase its length considerably. However, I have tried to provide an extensive collection of examples to arouse the reader's interest in applications, as well as sufficient citations to allow the interested reader to locate them. For the reader's convenience, an index to these citations is given at the end of the book .

Author : K. Glazek
Publisher : Springer Science & Business Media
Page : 394 pages
File Size : 51,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401599641

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A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences by K. Glazek Pdf

This volume presents a short guide to the extensive literature concerning semir ings along with a complete bibliography. The literature has been created over many years, in variety of languages, by authors representing different schools of mathematics and working in various related fields. In many instances the terminology used is not universal, which further compounds the difficulty of locating pertinent sources even in this age of the Internet and electronic dis semination of research results. So far there has been no single reference that could guide the interested scholar or student to the relevant publications. This book is an attempt to fill this gap. My interest in the theory of semirings began in the early sixties, when to gether with Bogdan W ~glorz I tried to investigate some algebraic aspects of compactifications of topological spaces, semirings of semicontinuous functions, and the general ideal theory for special semirings. (Unfortunately, local alge braists in Poland told me at that time that there was nothing interesting in investigating semiring theory because ring theory was still being developed). However, some time later we became aware of some similar investigations hav ing already been done. The theory of semirings has remained "my first love" ever since, and I have been interested in the results in this field that have been appearing in literature (even though I have not been active in this area myself).

Author : K. Glazek
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 47,9 Mb
Release : 2002-06-30
Category : Mathematics
ISBN : 1402007175

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A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences by K. Glazek Pdf

This book presents a guide to the extensive literature on the topic of semirings and includes a complete bibliography. It serves as a complement to the existing monographs and a point of reference to researchers and students on this topic. The literature on semirings has evolved over many years, in a variety of languages, by authors representing different schools of mathematics and working in various related fields. Recently, semiring theory has experienced rapid development, although publications are widely scattered. This survey also covers those newly emerged areas of semiring applications that have not received sufficient treatment in widely accessible monographs, as well as many lesser-known or `forgotten' works. The author has been collecting the bibliographic data for this book since 1985. Over the years, it has proved very useful for specialists. For example, J.S. Golan wrote he owed `... a special debt to Kazimierz Glazek, whose bibliography proved to be an invaluable guide to the bewildering maze of literature on semirings'. U. Hebisch and H.J. Weinert also mentioned his collection of literature had been of great assistance to them. Now updated to include publications up to the beginning of 2002, this work is available to a wide readership. Audience: This volume is the first single reference that can guide the interested scholar or student to the relevant publications in semirings, semifields, algebraic theory of languages and automata, positive matrices and other generalisations, and ordered semigroups and groups.

Author : Udo Hebisch,Hanns Joachim Weinert
Publisher : World Scientific
Page : 382 pages
File Size : 46,5 Mb
Release : 1998
Category : Mathematics
ISBN : 9810236018

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Semirings by Udo Hebisch,Hanns Joachim Weinert Pdf

This book provides an introduction to the algebraic theory of semirings, including a detailed treatment of some applications in theoretical computer science. The focus is on the general concepts and statements of the algebraic theory of semirings and those aspects of the theory which are needed for the aforementioned applications. The book also deals with a concept of semirings that includes commutativity of addition, as is usually done for rings.

Author : Jonathan S. Golan
Publisher : Springer Science & Business Media
Page : 243 pages
File Size : 42,6 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401703833

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Semirings and Affine Equations over Them by Jonathan S. Golan Pdf

Semiring theory stands with a foot in each of two mathematical domains. The first being abstract algebra and the other the fields of applied mathematics such as optimization theory, the theory of discrete-event dynamical systems, automata theory, and formal language theory, as well as from the allied areas of theoretical computer science and theoretical physics. Most important applications of semiring theory in these areas turn out to revolve around the problem of finding the equalizer of a pair of affine maps between two semimodules. In this volume, we chart the state of the art on solving this problem, and present many specific cases of applications. This book is essentially the third part of a trilogy, along with Semirings and their Applications, and Power Algebras over Semirings, both written by the same author and published by Kluwer Academic Publishers in 1999. While each book can be read independently of the others, to get the full force of the theory and applications one should have access to all three. This work will be of interest to academic and industrial researchers and graduate students. The intent of the book is to bring the applications to the attention of the abstract mathematicians and to make the abstract mathematics available to those who are using these tools in an ad-hoc manner without realizing the full force of the theory.

Author : Javed Ahsan,John N. Mordeson,Muhammad Shabir
Publisher : Springer
Page : 230 pages
File Size : 49,5 Mb
Release : 2012-03-05
Category : Technology & Engineering
ISBN : 9783642276415

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Fuzzy Semirings with Applications to Automata Theory by Javed Ahsan,John N. Mordeson,Muhammad Shabir Pdf

The purpose of this book is to present an up to date account of fuzzy ideals of a semiring. The book concentrates on theoretical aspects and consists of eleven chapters including three invited chapters. Among the invited chapters, two are devoted to applications of Semirings to automata theory, and one deals with some generalizations of Semirings. This volume may serve as a useful hand book for graduate students and researchers in the areas of Mathematics and Theoretical Computer Science.

Author : Michel Gondran,Michel Minoux
Publisher : Springer Science & Business Media
Page : 401 pages
File Size : 44,7 Mb
Release : 2008-05-14
Category : Business & Economics
ISBN : 9780387754505

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Graphs, Dioids and Semirings by Michel Gondran,Michel Minoux Pdf

The primary objective of this essential text is to emphasize the deep relations existing between the semiring and dioïd structures with graphs and their combinatorial properties. It does so at the same time as demonstrating the modeling and problem-solving flexibility of these structures. In addition the book provides an extensive overview of the mathematical properties employed by "nonclassical" algebraic structures which either extend usual algebra or form a new branch of it.

Author : Ronald R Yager,Ali M. Abbasov,Marek Z. Reformat,Shahnaz N Shahbazova
Publisher : Springer
Page : 316 pages
File Size : 47,6 Mb
Release : 2012-10-31
Category : Technology & Engineering
ISBN : 9783642349225

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Soft Computing: State of the Art Theory and Novel Applications by Ronald R Yager,Ali M. Abbasov,Marek Z. Reformat,Shahnaz N Shahbazova Pdf

This book is a tribute to Lotfi A. Zadeh, the father of fuzzy logic, on the occasion of his 90th Birthday. The book gathers original scientific contributions written by top scientists and presenting the latest theories, applications and new trends in the fascinating and challenging field of soft computing.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 52,7 Mb
Release : 2024-06-26
Category : Electronic
ISBN : 9789814470988

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Nonlinear Integrals and Their Applications in Data Mining by Anonim Pdf

Author : Cerstin Mahlow,Michael Piotrowski
Publisher : Springer Science & Business Media
Page : 147 pages
File Size : 43,5 Mb
Release : 2009-08-28
Category : Computers
ISBN : 9783642041310

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State of the Art in Computational Morphology by Cerstin Mahlow,Michael Piotrowski Pdf

From the point of view of computational linguistics, morphological resources are the basis for all higher-level applications. This is especially true for languages with a rich morphology, such as German or Finnish. A morphology component should thus be capable of analyzing single word forms as well as whole corpora. For many practical applications, not only morphological analysis, but also generation is required, i.e., the production of surfaces corresponding to speci?c categories. Apart from uses in computational linguistics, there are also numerous practical - plications that either require morphological analysis and generation or that can greatly bene?t from it, for example, in text processing, user interfaces, or information - trieval. These applications have speci?c requirements for morphological components, including requirements from software engineering, such as programming interfaces or robustness. In 1994, the First Morpholympics took place at the University of Erlangen- Nuremberg, a competition between several systems for the analysis and generation of German word forms. Eight systems participated in the First Morpholympics; the conference proceedings [1] thus give a very good overview of the state of the art in computational morphologyfor German as of 1994.

Author : Vassili N. Kolokoltsov,Victor P. Maslov
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 44,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401589017

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Idempotent Analysis and Its Applications by Vassili N. Kolokoltsov,Victor P. Maslov Pdf

The first chapter deals with idempotent analysis per se . To make the pres- tation self-contained, in the first two sections we define idempotent semirings, give a concise exposition of idempotent linear algebra, and survey some of its applications. Idempotent linear algebra studies the properties of the semirn- ules An , n E N , over a semiring A with idempotent addition; in other words, it studies systems of equations that are linear in an idempotent semiring. Pr- ably the first interesting and nontrivial idempotent semiring , namely, that of all languages over a finite alphabet, as well as linear equations in this sern- ing, was examined by S. Kleene [107] in 1956 . This noncommutative semiring was used in applications to compiling and parsing (see also [1]) . Presently, the literature on idempotent algebra and its applications to theoretical computer science (linguistic problems, finite automata, discrete event systems, and Petri nets), biomathematics, logic , mathematical physics , mathematical economics, and optimizat ion, is immense; e. g. , see [9, 10, 11, 12, 13, 15, 16 , 17, 22, 31 , 32, 35,36,37,38,39 ,40,41,52,53 ,54,55,61,62 ,63,64,68, 71, 72, 73,74,77,78, 79,80,81,82,83,84,85,86,88,114,125 ,128,135,136, 138,139,141,159,160, 167,170,173,174,175,176,177,178,179,180,185,186 , 187, 188, 189]. In §1. 2 we present the most important facts of the idempotent algebra formalism . The semimodules An are idempotent analogs of the finite-dimensional v- n, tor spaces lR and hence endomorphisms of these semi modules can naturally be called (idempotent) linear operators on An .

Author : Mariana Durcheva
Publisher : Cambridge Scholars Publishing
Page : 132 pages
File Size : 52,8 Mb
Release : 2019-11-12
Category : Mathematics
ISBN : 9781527543317

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Semirings as Building Blocks in Cryptography by Mariana Durcheva Pdf

Semirings as an algebraic structure have been known since 1934, but remained unapplied for mathematical purposes for a long time. It has only been in the past decade that they have been used in cryptography. The advantage of (additively) idempotent semirings is that the additive operation does not have an inverse, which can help in preventing the breakage of a cryptosystem. This book describes a number of cryptographic protocols, as well as the hard mathematical problems on which their security is based. It will appeal to cryptographers and specialists in applied algebra.

Author : Yo-Sub Han,Sang-Ki Ko
Publisher : Springer Nature
Page : 210 pages
File Size : 46,5 Mb
Release : 2022-01-01
Category : Computers
ISBN : 9783030934897

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Descriptional Complexity of Formal Systems by Yo-Sub Han,Sang-Ki Ko Pdf

This book constitutes the proceedings of the 23rd International Conference on Descriptional Complexity of Format Systems, DCFS 2021, which was supposed to take place in Seoul South Korea in June 2021, but the conference was canceled due to the COVID-19 crisis. The 16 full papers presented in this volume were carefully reviewed and selected from 21 submissions. The conference focus to all aspects of descriptional complexity-the costs of description of objects in various computational models such as Turing machines, pushdown automata, finite automata or grammars.

Author : Patricia Melin,Oscar Castillo,Janusz Kacprzyk,Marek Reformat,William Melek
Publisher : Springer
Page : 422 pages
File Size : 40,9 Mb
Release : 2017-09-30
Category : Technology & Engineering
ISBN : 9783319671376

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Fuzzy Logic in Intelligent System Design by Patricia Melin,Oscar Castillo,Janusz Kacprzyk,Marek Reformat,William Melek Pdf

This book describes recent advances in the use of fuzzy logic for the design of hybrid intelligent systems based on nature-inspired optimization and their applications in areas such as intelligent control and robotics, pattern recognition, medical diagnosis, time series prediction and optimization of complex problems. Based on papers presented at the North American Fuzzy Information Processing Society Annual Conference (NAFIPS 2017), held in Cancun, Mexico from 16 to 18 October 2017, the book is divided into nine main parts, the first of which first addresses theoretical aspects, and proposes new concepts and algorithms based on type-1 fuzzy systems. The second part consists of papers on new concepts and algorithms for type-2 fuzzy systems, and on applications of type-2 fuzzy systems in diverse areas, such as time series prediction and pattern recognition. In turn, the third part contains papers that present enhancements to meta-heuristics based on fuzzy logic techniques describing new nature-inspired optimization algorithms that use fuzzy dynamic adaptation of parameters. The fourth part presents emergent intelligent models, which range from quantum algorithms to cellular automata. The fifth part explores applications of fuzzy logic in diverse areas of medicine, such as the diagnosis of hypertension and heart diseases. The sixth part describes new computational intelligence algorithms and their applications in different areas of intelligent control, while the seventh examines the use of fuzzy logic in different mathematic models. The eight part deals with a diverse range of applications of fuzzy logic, ranging from environmental to autonomous navigation, while the ninth covers theoretical concepts of fuzzy models

Author : Jana, Chiranjibe,Senapati, Tapan,Pal, Madhumangal
Publisher : IGI Global
Page : 439 pages
File Size : 50,5 Mb
Release : 2019-10-25
Category : Mathematics
ISBN : 9781799801924

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Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures by Jana, Chiranjibe,Senapati, Tapan,Pal, Madhumangal Pdf

In the world of mathematics, the study of fuzzy relations and its theories are well-documented and a staple in the area of calculative methods. What many researchers and scientists overlook is how fuzzy theory can be applied to industries outside of arithmetic. The framework of fuzzy logic is much broader than professionals realize. There is a lack of research on the full potential this theoretical model can reach. The Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures provides emerging research exploring the theoretical and practical aspects of fuzzy set theory and its real-life applications within the fields of engineering and science. Featuring coverage on a broad range of topics such as complex systems, topological spaces, and linear transformations, this book is ideally designed for academicians, professionals, and students seeking current research on innovations in fuzzy logic in algebra and other matrices.