Semirings

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Semirings: Algebraic Theory And Applications In Computer Science

Author : Hanns Joachim Weinert
Publisher : World Scientific
ISBN 13 : 9814495697
Total Pages : 371 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Semirings: Algebraic Theory And Applications In Computer Science by : Hanns Joachim Weinert

Download or read book Semirings: Algebraic Theory And Applications In Computer Science written by Hanns Joachim Weinert and published by World Scientific. This book was released on 1998-10-30 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the algebraic theory of semirings and, in this context, to basic algebraic concepts as e.g. semigroups, lattices and rings. It includes an algebraic theory of infinite sums as well as a detailed treatment of several applications in theoretical computer science. Complete proofs, various examples and exercises (some of them with solutions) make the book suitable for self-study. On the other hand, a more experienced reader who looks for information about the most common concepts and results on semirings will find cross-references throughout the book, a comprehensive bibliography and various hints to it.

Semirings and their Applications

Author : Jonathan S. Golan
Publisher : Springer Science & Business Media
ISBN 13 : 9780792357865
Total Pages : 404 pages
Book Rating : 4.3/5 (578 download)

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Book Synopsis Semirings and their Applications by : Jonathan S. Golan

Download or read book Semirings and their Applications written by Jonathan S. Golan and published by Springer Science & Business Media. This book was released on 1999-07-31 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is an updated and considerably expanded version of the author's book The Theory of Semirings, with Applications to Mathematics and Theoretical Science, which has been recognized as the definitive reference work in this area. This edition includes many of the new results in this area, as well as further applications of semiring theory in such areas as idempotent analysis, discrete dynamical systems, formal language theory, fuzzy set theory, optimization etc. The book contains an extensive bibliography and a large number of examples. Audience: This book is aimed both at mathematicians and at researchers in applied mathematics and theoretical computer science. It is also suitable for use as a graduate-level textbook.

A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences

Author : K. Glazek
Publisher : Springer Science & Business Media
ISBN 13 : 9401599645
Total Pages : 394 pages
Book Rating : 4.4/5 (15 download)

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

Download or read book A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences written by K. Glazek and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Semirings and their Applications

Author : Jonathan S. Golan
Publisher : Springer Science & Business Media
ISBN 13 : 9401593337
Total Pages : 376 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Semirings and their Applications by : Jonathan S. Golan

Download or read book Semirings and their Applications written by Jonathan S. Golan and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 .

Power Algebras over Semirings

Author : Jonathan S. Golan
Publisher : Springer Science & Business Media
ISBN 13 : 9401592411
Total Pages : 207 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Power Algebras over Semirings by : Jonathan S. Golan

Download or read book Power Algebras over Semirings written by Jonathan S. Golan and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a continuation of several themes presented in my previous books [146, 149]. In those volumes, I was concerned primarily with the properties of semirings. Here, the objects of investigation are sets of the form RA, where R is a semiring and A is a set having a certain structure. The problem is one of translating that structure to RA in some "natural" way. As such, it tries to find a unified way of dealing with diverse topics in mathematics and theoretical com puter science as formal language theory, the theory of fuzzy algebraic structures, models of optimal control, and many others. Another special case is the creation of "idempotent analysis" and similar work in optimization theory. Unlike the case of the previous work, which rested on a fairly established mathematical foundation, the approach here is much more tentative and docimastic. This is an introduction to, not a definitative presentation of, an area of mathematics still very much in the making. The basic philosphical problem lurking in the background is one stated suc cinctly by Hahle and Sostak [185]: ". . . to what extent basic fields of mathematics like algebra and topology are dependent on the underlying set theory?" The conflicting definitions proposed by various researchers in search of a resolution to this conundrum show just how difficult this problem is to see in a proper light.

Semirings and Affine Equations over Them

Author : Jonathan S. Golan
Publisher : Springer Science & Business Media
ISBN 13 : 9401703833
Total Pages : 243 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Semirings and Affine Equations over Them by : Jonathan S. Golan

Download or read book Semirings and Affine Equations over Them written by Jonathan S. Golan and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Graphs, Dioids and Semirings

Author : Michel Gondran
Publisher : Springer Science & Business Media
ISBN 13 : 0387754504
Total Pages : 401 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Graphs, Dioids and Semirings by : Michel Gondran

Download or read book Graphs, Dioids and Semirings written by Michel Gondran and published by Springer Science & Business Media. This book was released on 2008-05-14 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Smarandache Semirings, Semifields, and Semivector Spaces

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1931233624
Total Pages : 122 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Smarandache Semirings, Semifields, and Semivector Spaces by : W. B. Vasantha Kandasamy

Download or read book Smarandache Semirings, Semifields, and Semivector Spaces written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2002 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fuzzy Semirings with Applications to Automata Theory

Author : Javed Ahsan
Publisher : Springer Science & Business Media
ISBN 13 : 3642276407
Total Pages : 234 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Fuzzy Semirings with Applications to Automata Theory by : Javed Ahsan

Download or read book Fuzzy Semirings with Applications to Automata Theory written by Javed Ahsan and published by Springer Science & Business Media. This book was released on 2012-03-14 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Interval Semirings

Author : W. B. Vasantha Kandasamy, Florentin Smarandache
Publisher : Infinite Study
ISBN 13 : 1599730332
Total Pages : 157 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Interval Semirings by : W. B. Vasantha Kandasamy, Florentin Smarandache

Download or read book Interval Semirings written by W. B. Vasantha Kandasamy, Florentin Smarandache and published by Infinite Study. This book was released on 2011 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the new notion of interval semirings are introduced. New structures like interval groups are used to construct interval group semirings. Further non-associative interval semirings are constructed using loops and groupoids. We have given 284 examples, 118 problems are proposed ¿ some of them at the research level.The main keywords are interval semirings, interval groups, interval matrix semirings, interval groupoid semirings, neutrosophic interval semirings, and loop interval semirings.

Subset Non Associative Semirings

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1599732254
Total Pages : 209 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Subset Non Associative Semirings by : W. B. Vasantha Kandasamy

Download or read book Subset Non Associative Semirings written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Semirings as Building Blocks in Cryptography

Author : Mariana Durcheva
Publisher : Cambridge Scholars Publishing
ISBN 13 : 1527543315
Total Pages : 132 pages
Book Rating : 4.5/5 (275 download)

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Book Synopsis Semirings as Building Blocks in Cryptography by : Mariana Durcheva

Download or read book Semirings as Building Blocks in Cryptography written by Mariana Durcheva and published by Cambridge Scholars Publishing. This book was released on 2019-11-12 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Semirings for Soft Constraint Solving and Programming

Author : Stefano Bistarelli
Publisher : Springer Science & Business Media
ISBN 13 : 3540211810
Total Pages : 292 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Semirings for Soft Constraint Solving and Programming by : Stefano Bistarelli

Download or read book Semirings for Soft Constraint Solving and Programming written by Stefano Bistarelli and published by Springer Science & Business Media. This book was released on 2004-02-24 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Constraint satisfaction and constraint programming have shown to be very simple but powerful ideas, with applications in various areas. Still, in the last ten years, the simple notion of constraints has shown some deficiencies concerning both theory and practice, typically in the way over-constrained problems and preferences are treated. For this reason, the notion of soft constraints has been introduced with semiring-based soft constraints and valued constraints being the two main general frameworks. This book includes formal definitions and properties of semiring-based soft constraints, as well as their use within constraint logic programming and concurrent constraint programming. Moreover, the author shows how to adapt existing notions and techniques such as abstraction and interchangeability to the soft constraint framework and it is demonstrated how soft constraints can be used in some application areas, such as security. Overall, this book is a great starting point for anyone interested in understanding the basics of semiring-based soft constraints.

A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences

Author : K. Glazek
Publisher : Springer Science & Business Media
ISBN 13 : 9781402007170
Total Pages : 404 pages
Book Rating : 4.0/5 (71 download)

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

Download or read book A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences written by K. Glazek and published by Springer Science & Business Media. This book was released on 2002-06-30 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Developments in Language Theory

Author : Masami Ito
Publisher : Springer
ISBN 13 : 354085780X
Total Pages : 555 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Developments in Language Theory by : Masami Ito

Download or read book Developments in Language Theory written by Masami Ito and published by Springer. This book was released on 2008-09-10 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 12th International Conference on Developments in Language Theory, DLT 2008, held in Kyoto, Japan, September 2008. The 36 revised full papers presented together with 6 invited papers were carefully reviewed and selected from 102 submissions. All important issues in language theory are addressed including grammars, acceptors and transducers for words, trees and graphs; algebraic theories of automata; algorithmic, combinatorial and algebraic properties of words and languages; variable length codes; symbolic dynamics; cellular automata; polyominoes and multidimensional patterns; decidability questions; image manipulation and compression; efficient text algorithms; relationships to cryptography, concurrency, complexity theory and logic; bio-inspired computing; quantum computing.

Relations and Kleene Algebra in Computer Science

Author : Rudolf Berghammer
Publisher : Springer Science & Business Media
ISBN 13 : 354078912X
Total Pages : 406 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Relations and Kleene Algebra in Computer Science by : Rudolf Berghammer

Download or read book Relations and Kleene Algebra in Computer Science written by Rudolf Berghammer and published by Springer Science & Business Media. This book was released on 2008-03-28 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book constitutes the joint refereed proceedings of the 10th International Conference on Relational Methods in Computer Science, RelMiCS 2008, and the 5th International Conference on Applications of Kleene Algebras, AKA 2008, held in Manchester, UK in April 2008. The 26 revised full papers presented together with 2 invited papers were carefully reviewed and selected from numerous submissions. The papers describe the calculus of relations and similar algebraic formalisms as methodological and conceptual tools with special focus on formal methods for software engineering, logics of programs and links to neighbouring disciplines. Their scope comprises relation algebra, fixpoint calculi, semiring theory, iteration algebras, process algebras and dynamic algebras. Applications include formal algebraic modeling, the semantics, analysis and development of programs, formal language theory and combinatorial optimization.

Algebraic Methodology and Software Technology

Author : José Meseguer
Publisher : Springer Science & Business Media
ISBN 13 : 3540799796
Total Pages : 442 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Algebraic Methodology and Software Technology by : José Meseguer

Download or read book Algebraic Methodology and Software Technology written by José Meseguer and published by Springer Science & Business Media. This book was released on 2008-07-15 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 12th International Conference on Algebraic Methodology and Software Technology, AMAST 2008, held in Urbana, IL, USA, in July 2008. The 28 revised full papers presented together with 3 invited talks were carefully reviewed and selected from 58 submissions. Among the topics covered are all current issues in formal methods related to algebraic and logical foundations, software technology, and to programming methodology including concurrent and reactive systems, evolutionary software/adaptive systems, logic and functional programming, object paradigms, constraint programming and concurrency, program verification and transformation, programming calculi, specification languages and tools, formal specification and development case studies, logic, category theory, relation algebra, computational algebra, algebraic foundations for languages and systems, coinduction, theorem proving and logical frameworks for reasoning, logics of programs, as well as algebra and coalgebra.