Universal Algebra And Applications In Theoretical Computer Science
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Universal Algebra And Applications In Theoretical Computer Science
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Author : Klaus Denecke
language : en
Publisher: CRC Press
Release Date : 2002-01-18
Universal Algebra And Applications In Theoretical Computer Science written by Klaus Denecke and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-18 with Mathematics categories.
Over the past 20 years, the emergence of clone theory, hyperequational theory, commutator theory and tame congruence theory has led to a growth of universal algebra both in richness and in applications, especially in computer science. Yet most of the classic books on the subject are long out of print and, to date, no other book has integrated these theories with the long-established work that supports them. Universal Algebra and Applications in Theoretical Computer Science introduces the basic concepts of universal algebra and surveys some of the newer developments in the field. The first half of the book provides a solid grounding in the core material. A leisurely pace, careful exposition, numerous examples, and exercises combine to form an introduction to the subject ideal for beginning graduate students or researchers from other areas. The second half of the book focuses on applications in theoretical computer science and advanced topics, including Mal'cev conditions, tame congruence theory, clones, and commutators. The impact of the advances in universal algebra on computer science is just beginning to be realized, and the field will undoubtedly continue to grow and mature. Universal Algebra and Applications in Theoretical Computer Science forms an outstanding text and offers a unique opportunity to build the foundation needed for further developments in its theory and in its computer science applications.
Universal Algebra For Computer Scientists
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Author : Wolfgang Wechler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Universal Algebra For Computer Scientists written by Wolfgang Wechler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
A new model-theoretic approach to universal algebra is offered in this book. Written for computer scientists, it presents a systematic development of the methods and results of universal algebra that are useful in a variety of applications in computer science. The notation is simple and the concepts are clearly presented. The book concerns the algebraic characterization of axiomatic classes of algebras (equational, implicational, and universal Horn classes) by closure operators generalizing the famous Birkhoff Variety Theorem, and the algebraic characterization of the related theories. The book also presents a thorough study of term rewriting systems. Besides basic notions, the Knuth-Bendix completion procedure and termination proof methods are considered. A third main topic is that of fixpoint techniques and complete ordered algebras. Algebraic specifications of abstract data types and algebraic semantics of recursive program schemes are treated as applications. The book is self-contained and suitable both as a textbook for graduate courses and as a reference for researchers.
Finite Semigroups And Universal Algebra
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Author : Jorge Almeida
language : en
Publisher: World Scientific
Release Date : 1995-01-27
Finite Semigroups And Universal Algebra written by Jorge Almeida and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-27 with Mathematics categories.
Motivated by applications in theoretical computer science, the theory of finite semigroups has emerged in recent years as an autonomous area of mathematics. It fruitfully combines methods, ideas and constructions from algebra, combinatorics, logic and topology. In simple terms, the theory aims at a classification of finite semigroups in certain classes called “pseudovarieties”. The classifying characteristics have both structural and syntactical aspects, the general connection between them being part of universal algebra. Besides providing a foundational study of the theory in the setting of arbitrary abstract finite algebras, this book stresses the syntactical approach to finite semigroups. This involves studying (relatively) free and profinite free semigroups and their presentations. The techniques used are illustrated in a systematic study of various operators on pseudovarieties of semigroups.
Semirings
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Author : Udo Hebisch
language : en
Publisher: World Scientific
Release Date : 1998
Semirings written by Udo Hebisch and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
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.
Geometric Computing With Clifford Algebras
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Author : Gerald Sommer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Geometric Computing With Clifford Algebras written by Gerald Sommer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Computers categories.
Clifford algebra, then called geometric algebra, was introduced more than a cenetury ago by William K. Clifford, building on work by Grassmann and Hamilton. Clifford or geometric algebra shows strong unifying aspects and turned out in the 1960s to be a most adequate formalism for describing different geometry-related algebraic systems as specializations of one "mother algebra" in various subfields of physics and engineering. Recent work outlines that Clifford algebra provides a universal and powerfull algebraic framework for an elegant and coherent representation of various problems occuring in computer science, signal processing, neural computing, image processing, pattern recognition, computer vision, and robotics. This monograph-like anthology introduces the concepts and framework of Clifford algebra and provides computer scientists, engineers, physicists, and mathematicians with a rich source of examples of how to work with this formalism.
A Course In Universal Algebra
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Author : S. Burris
language : en
Publisher: Springer
Release Date : 2011-10-21
A Course In Universal Algebra written by S. Burris and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-21 with Mathematics categories.
Universal algebra has enjoyed a particularly explosive growth in the last twenty years, and a student entering the subject now will find a bewildering amount of material to digest. This text is not intended to be encyclopedic; rather, a few themes central to universal algebra have been developed sufficiently to bring the reader to the brink of current research. The choice of topics most certainly reflects the authors' interests. Chapter I contains a brief but substantial introduction to lattices, and to the close connection between complete lattices and closure operators. In particular, everything necessary for the subsequent study of congruence lattices is included. Chapter II develops the most general and fundamental notions of uni versal algebra-these include the results that apply to all types of algebras, such as the homomorphism and isomorphism theorems. Free algebras are discussed in great detail-we use them to derive the existence of simple algebras, the rules of equational logic, and the important Mal'cev conditions. We introduce the notion of classifying a variety by properties of (the lattices of) congruences on members of the variety. Also, the center of an algebra is defined and used to characterize modules (up to polynomial equivalence). In Chapter III we show how neatly two famous results-the refutation of Euler's conjecture on orthogonal Latin squares and Kleene's character ization of languages accepted by finite automata-can be presented using universal algebra. We predict that such "applied universal algebra" will become much more prominent.
Algebras And Orders
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Author : Ivo G. Rosenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Algebras And Orders written by Ivo G. Rosenberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
In the summer of 1991 the Department of Mathematics and Statistics of the Universite de Montreal was fortunate to host the NATO Advanced Study Institute "Algebras and Orders" as its 30th Seminaire de mathematiques superieures (SMS), a summer school with a long tradition and well-established reputation. This book contains the contributions of the invited speakers. Universal algebra- which established itself only in the 1930's- grew from traditional algebra (e.g., groups, modules, rings and lattices) and logic (e.g., propositional calculus, model theory and the theory of relations). It started by extending results from these fields but by now it is a well-established and dynamic discipline in its own right. One of the objectives of the ASI was to cover a broad spectrum of topics in this field, and to put in evidence the natural links to, and interactions with, boolean algebra, lattice theory, topology, graphs, relations, automata, theoretical computer science and (partial) orders. The theory of orders is a relatively young and vigorous discipline sharing certain topics as well as many researchers and meetings with universal algebra and lattice theory. W. Taylor surveyed the abstract clone theory which formalizes the process of compos ing operations (i.e., the formation of term operations) of an algebra as a special category with countably many objects, and leading naturally to the interpretation and equivalence of varieties.
Fst Tcs 2003 Foundations Of Software Technology And Theoretical Computer Science
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Author : Paritosh K Pandya
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-12-03
Fst Tcs 2003 Foundations Of Software Technology And Theoretical Computer Science written by Paritosh K Pandya and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-03 with Computers categories.
This book constitutes the refereed proceedings of the 23rd Conference on Foundations of Software Technology and Theoretical Computer Science, FST TCS 2003, held in Mumbai, India in December 2003. The 23 revised full papers presented together with 4 invited papers and the abstract of an invited paper were carefully reviewed and selected from 160 submissions. A broad variety of current topics from the theory of computing are addressed, ranging from algorithmics and discrete mathematics to logics and programming theory.
Theory Of Generalized Inverses Over Commutative Rings
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Author : K.P.S. Bhaskara Rao
language : en
Publisher: CRC Press
Release Date : 2002-03-21
Theory Of Generalized Inverses Over Commutative Rings written by K.P.S. Bhaskara Rao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-03-21 with Mathematics categories.
The theory of generalized inverses of real or complex matrices has been expertly developed and documented. But the generalized inverses of matrices over rings have received comprehensive treatment only recently. In this book, the author, who contributed to the research and development of the theory, explains his results. The subject of generalized inverses of matrices over rings has now reached a state suitable for a comprehensive treatment - this book provides just that, for mathematicians, algebraists and control theorists.
Algebra And Coalgebra In Computer Science
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Author : Alexander Kurz
language : en
Publisher: Springer
Release Date : 2009-09-19
Algebra And Coalgebra In Computer Science written by Alexander Kurz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-19 with Computers categories.
This book constitutes the proceedings of the Third International Conference on Algebra and Coalgebra in Computer Science, CALCO 2009, formed in 2005 by joining CMCS and WADT. This year the conference was held in Udine, Italy, September 7-10, 2009. The 23 full papers were carefully reviewed and selected from 42 submissions. They are presented together with four invited talks and workshop papers from the CALCO-tools Workshop. The conference was divided into the following sessions: algebraic effects and recursive equations, theory of coalgebra, coinduction, bisimulation, stone duality, game theory, graph transformation, and software development techniques.