Universal Algebra And Applications In Theoretical Computer Science
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Author | : Klaus Denecke |
Publisher | : CRC Press |
Total Pages | : 396 |
Release | : 2018-10-03 |
Genre | : Mathematics |
ISBN | : 1482285835 |
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.
Author | : Wolfgang Wechler |
Publisher | : Springer Science & Business Media |
Total Pages | : 345 |
Release | : 2012-12-06 |
Genre | : Computers |
ISBN | : 3642767710 |
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.
Author | : George Grätzer |
Publisher | : Springer Science & Business Media |
Total Pages | : 601 |
Release | : 2008-12-15 |
Genre | : Mathematics |
ISBN | : 0387774874 |
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.
Author | : Delaram Kahrobaei |
Publisher | : American Mathematical Soc. |
Total Pages | : 242 |
Release | : 2016-11-28 |
Genre | : Mathematics |
ISBN | : 1470423030 |
This volume contains the proceedings of three special sessions: Algebra and Computer Science, held during the Joint AMS-EMS-SPM meeting in Porto, Portugal, June 10–13, 2015; Groups, Algorithms, and Cryptography, held during the Joint Mathematics Meeting in San Antonio, TX, January 10–13, 2015; and Applications of Algebra to Cryptography, held during the Joint AMS-Israel Mathematical Union meeting in Tel-Aviv, Israel, June 16–19, 2014. Papers contained in this volume address a wide range of topics, from theoretical aspects of algebra, namely group theory, universal algebra and related areas, to applications in several different areas of computer science. From the computational side, the book aims to reflect the rapidly emerging area of algorithmic problems in algebra, their computational complexity and applications, including information security, constraint satisfaction problems, and decision theory. The book gives special attention to recent advances in quantum computing that highlight the need for a variety of new intractability assumptions and have resulted in a new area called group-based cryptography.
Author | : Jorge Almeida |
Publisher | : World Scientific |
Total Pages | : 532 |
Release | : 1995-01-27 |
Genre | : Mathematics |
ISBN | : 9814501565 |
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.
Author | : Klaus Denecke |
Publisher | : World Scientific |
Total Pages | : 291 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 9812837450 |
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.
Author | : Clifford Bergman |
Publisher | : CRC Press |
Total Pages | : 324 |
Release | : 2011-09-20 |
Genre | : Computers |
ISBN | : 1439851298 |
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 of universal algebra and by introducing a variety of recent research topics. The first part of the book focuses on core components, including subalgebras, congruences, lattices, direct and subdirect products, isomorphism theorems, a clone of operations, terms, free algebras, Birkhoff’s theorem, and standard Maltsev conditions. The second part covers topics that demonstrate the power and breadth of the subject. The author discusses the consequences of Jónsson’s lemma, finitely and nonfinitely based algebras, definable principal congruences, and the work of Foster and Pixley on primal and quasiprimal algebras. He also includes a proof of Murskiĭ’s theorem on primal algebras and presents McKenzie’s characterization of directly representable varieties, which clearly shows the power of the universal algebraic toolbox. The last chapter covers the rudiments of tame congruence theory. Throughout the text, a series of examples illustrates concepts as they are introduced and helps students understand how universal algebra sheds light on topics they have already studied, such as Abelian groups and commutative rings. Suitable for newcomers to the field, the book also includes carefully selected exercises that reinforce the concepts and push students to a deeper understanding of the theorems and techniques.
Author | : George Grätzer |
Publisher | : Springer |
Total Pages | : 583 |
Release | : 1979-08-06 |
Genre | : Mathematics |
ISBN | : 9780387903552 |
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.
Author | : Lars Garding |
Publisher | : Springer |
Total Pages | : 214 |
Release | : 1988-08 |
Genre | : Computers |
ISBN | : |
A concise presentation of number theory, algebra, and group theory and their applications to some parts of Computer Science, among them the finite Fourier transform, algebraic complexity theory, coding, Boolean algebra, monoids and rational languages. A judicious choice of exercises has made it possible to cover a large amount of material without sacrificing readability. The book is intended primarily for use in Computer Science, but it may also serve for intermediate algebra courses with selected applications, .
Author | : Jörg Koppitz |
Publisher | : Springer Science & Business Media |
Total Pages | : 364 |
Release | : 2006-02-10 |
Genre | : Mathematics |
ISBN | : 9780387308043 |
A complete and systematic introduction to the fundamentals of the hyperequational theory of universal algebra, offering the newest results on solid varieties of semirings and semigroups. The book aims to develop the theory of solid varieties as a system of mathematical discourse that is applicable in several concrete situations. A unique feature of this book is the use of Galois connections to integrate different topics.