Universal Algebra For Computer Scientists

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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.

Universal Algebra For Computer Scientists

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Author : Wolfgang Wechler
language : en
Publisher: Springer
Release Date : 2012-08-01

Universal Algebra For Computer Scientists written by Wolfgang Wechler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-01 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.

Universal Algebra And Applications In Theoretical Computer Science

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Author : Klaus Denecke
language : en
Publisher: CRC Press
Release Date : 2018-10-03

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 2018-10-03 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.

Don Pigozzi On Abstract Algebraic Logic Universal Algebra And Computer Science

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Author : Janusz Czelakowski
language : en
Publisher: Springer
Release Date : 2018-03-20

Don Pigozzi On Abstract Algebraic Logic Universal Algebra And Computer Science written by Janusz Czelakowski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-20 with Philosophy categories.

This book celebrates the work of Don Pigozzi on the occasion of his 80th birthday. In addition to articles written by leading specialists and his disciples, it presents Pigozzi’s scientific output and discusses his impact on the development of science. The book both catalogues his works and offers an extensive profile of Pigozzi as a person, sketching the most important events, not only related to his scientific activity, but also from his personal life. It reflects Pigozzi's contribution to the rise and development of areas such as abstract algebraic logic (AAL), universal algebra and computer science, and introduces new scientific results. Some of the papers also present chronologically ordered facts relating to the development of the disciplines he contributed to, especially abstract algebraic logic. The book offers valuable source material for historians of science, especially those interested in history of mathematics and logic.

Universal Algebra

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Author : George Grätzer
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-15

Universal Algebra written by George Grätzer 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 2008-12-15 with Mathematics categories.

Universal Algebra has become the most authoritative, consistently relied on text in a field with applications in other branches of algebra and other fields such as combinatorics, geometry, and computer science. Each chapter is followed by an extensive list of exercises and problems. The "state of the art" account also includes new appendices (with contributions from B. Jónsson, R. Quackenbush, W. Taylor, and G. Wenzel) and a well selected additional bibliography of over 1250 papers and books which makes this an indispensable new edition for students, faculty, and workers in the field.

Universal Algebra And Coalgebra

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Author : Klaus Denecke
language : en
Publisher: World Scientific
Release Date : 2009

Universal Algebra And Coalgebra written by Klaus Denecke and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

The purpose of this book is to study the structures needed to model objects in universal algebra, universal coalgebra and theoretical computer science. Universal algebra is used to describe different kinds of algebraic structures, while coalgebras are used to model state-based machines in computer science.The connection between algebras and coalgebras provides a way to connect static data-oriented systems with dynamical behavior-oriented systems. Algebras are used to describe data types and coalgebras describe abstract systems or machines.The book presents a clear overview of the area, from which further study may proceed.

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.

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.

Universal Algebra

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Author : Clifford Bergman
language : en
Publisher: CRC Press
Release Date : 2011-09-20

Universal Algebra written by Clifford Bergman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-20 with Computers categories.

Starting with the most basic notions, Universal Algebra: Fundamentals and Selected Topics introduces all the key elements needed to read and understand current research in this field. Based on the author's two-semester course, the text prepares students for research work by providing a solid grounding in the fundamental constructions and concepts o

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.