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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...
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 ...
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 optimizati...
It is by no means clear what comprises the "heart" or "core" of algebra, the part of algebra which every algebraist should know. Hence we feel that a book on "our heart" might be useful. We have tried to catch this heart in a collection of about 150 short sections, written by leading algebraists in these areas. These sections are organized in 9 chapters A, B, . . . , I. Of course, the selection is partly based on personal preferences, and we ask you for your understanding if some selections do not meet your taste (for unknown reasons, we only had problems in the chapter "Groups" to get enough articles in time). We hope that this book sets up a standard of what all algebraists are supposed to...
These proceedings contain the final versions of the papers presented at the 7th International Workshop on Finite-State Methods and Natural Language Processing (FSMNLP), held in Ispra, Italy, on September 11–12, 2008. The aim of the FSMNLP workshops is to bring together members of the research and industrial community working on finite-state based models in language technology, computational linguistics, web mining, linguistics and cognitive science on one hand, and on related theory and methods in fields such as computer science and mathematics on the other. Thus, the workshop series is a forum for researchers and practitioners working on applications as well as theoretical and implementat...
This book contains selected state-of-the-art contributions to the 9th conference on natural language processing, KONVENS 2008 (Konferenz zur Verarbeitung natürlicher Sprache), with the central theme: text resources and lexical knowledge. The collection is unique in its placement of focus on the interaction between both of the above-mentioned fields, illustrating in particular the importance of methods in corpus linguistics for building lexical resources on the one hand, and the relevance of lexical resources for the analysis of and intelligent search methods for text corpora on the other. The selected articles all present novel approaches to one of three different research areas which in turn define the three parts of the book: Techniques and models for the linguistic analysis of text resources: contributions from computational linguistics Methods and tools for the acquisition of lexical knowledge from digitized and linguistically annotated text resources Approaches to the representation of lexical knowledge in digital media for various purposes.
Part I (eleven chapters) of this text for graduate students provides a Survey of topological fields, while Part II (five chapters) provides a relatively more idiosyncratic account of valuation theory.
This book is an outcome of the conference on ordered algebraic structures held at Nanjing. It covers a range of topics: lattice theory, ordered semi groups, partially ordered groups, totally ordered groups, lattice-ordered groups, and ordered fields.