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Universal Algebra For Computer Scientists
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Book Synopsis Universal Algebra for Computer Scientists by : Wolfgang Wechler
Download or read book Universal Algebra for Computer Scientists written by Wolfgang Wechler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Universal Algebra and Applications in Theoretical Computer Science by : Klaus Denecke
Download or read book Universal Algebra and Applications in Theoretical Computer Science written by Klaus Denecke and published by CRC Press. This book was released on 2018-10-03 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science by : Janusz Czelakowski
Download or read book Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science written by Janusz Czelakowski and published by Springer. This book was released on 2018-03-20 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Universal Algebra and Coalgebra by : Klaus Denecke
Download or read book Universal Algebra and Coalgebra written by Klaus Denecke and published by World Scientific. This book was released on 2009 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Official Summary of Security Transactions and Holdings Reported to the Securities and Exchange Commission Under the Securities Exchange Act of 1934 and the Public Utility Holding Company Act of 1935 by : United States. Securities and Exchange Commission
Download or read book Official Summary of Security Transactions and Holdings Reported to the Securities and Exchange Commission Under the Securities Exchange Act of 1934 and the Public Utility Holding Company Act of 1935 written by United States. Securities and Exchange Commission and published by . This book was released on 1988 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematics for Computer Science by : Eric Lehman
Download or read book Mathematics for Computer Science written by Eric Lehman and published by . This book was released on 2017-03-08 with total page 988 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.
Book Synopsis Algebraic Logic and Universal Algebra in Computer Science by : Clifford H. Bergman
Download or read book Algebraic Logic and Universal Algebra in Computer Science written by Clifford H. Bergman and published by Springer. This book was released on 2000-11-13 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Semigroups and Universal Algebra by : Jorge Almeida
Download or read book Finite Semigroups and Universal Algebra written by Jorge Almeida and published by World Scientific. This book was released on 1995-01-27 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Contents:Finite Universal Algebra:Elements of Universal AlgebraOrder and TopologyFinite AlgebrasDecidabilityFinite Semigroups and Monoids:PreliminariesPermutativityOperators Relating Semigroups and MonoidsSemigroups Whose Regular D-Classes are SubsemigroupsThe JoinThe Semidirect ProductThe PowerFactorization of Implicit OperationsOpen Problems Readership: Mathematicians and computer scientists. keywords:Inite Semigroups;Finite Monoids;Universal Algebra;Recognizable Languages;Pseudovarieties;Pseudoidentities;Implicit Operations;Relatively Free Profinite Semigroups;Semidirect Products;Power Semigroups “This book is devoted to an exciting new field where author has made important contributions, and thus it is a most welcome addition to the existing literature. It will find its place on the bookshelves of many a specialist in semigroups, as well as species of algebraists and computer scientists, including graduate students.” Semigroup Forum “The book … constitutes an important contribution to the most active part of the present theory of finite semigroups. All overwhelming majority of the results included in it is very new and has been scattered over journals so far. The book does not cover all of the theory of semigroup … but it is extremely rich in material and ideas presented with skill and dedication. The book has already influenced the area essentially, and its influence will certainly grow … I think the book is a must for researchers in the area but it is also very useful for all those who want to trace modern developments in the theory of semigroups.” Mathematics Abstracts
Book Synopsis Basic Category Theory for Computer Scientists by : Benjamin C. Pierce
Download or read book Basic Category Theory for Computer Scientists written by Benjamin C. Pierce and published by MIT Press. This book was released on 1991-08-07 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Contents Tutorial • Applications • Further Reading
Book Synopsis A Course in Universal Algebra by : S. Burris
Download or read book A Course in Universal Algebra written by S. Burris and published by Springer. This book was released on 2011-10-21 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Relational and Algebraic Methods in Computer Science by : Uli Fahrenberg
Download or read book Relational and Algebraic Methods in Computer Science written by Uli Fahrenberg and published by Springer Nature. This book was released on 2021-10-22 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 19th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2021, which took place in Marseille, France, during November 2-5, 2021. The 29 papers presented in this book were carefully reviewed and selected from 35 submissions. They deal with the development and dissemination of relation algebras, Kleene algebras, and similar algebraic formalisms. Topics covered range from mathematical foundations to applications as conceptual and methodological tools in computer science and beyond.
Book Synopsis Algebraic Logic and Universal Algebra in Computer Science by : Clifford H. Bergman
Download or read book Algebraic Logic and Universal Algebra in Computer Science written by Clifford H. Bergman and published by . This book was released on 1990 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Universal Algebra by : George Grätzer
Download or read book Universal Algebra written by George Grätzer and published by Springer Science & Business Media. This book was released on 2008-12-15 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Foundations of Algebraic Specification and Formal Software Development by : Donald Sannella
Download or read book Foundations of Algebraic Specification and Formal Software Development written by Donald Sannella and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides foundations for software specification and formal software development from the perspective of work on algebraic specification, concentrating on developing basic concepts and studying their fundamental properties. These foundations are built on a solid mathematical basis, using elements of universal algebra, category theory and logic, and this mathematical toolbox provides a convenient language for precisely formulating the concepts involved in software specification and development. Once formally defined, these notions become subject to mathematical investigation, and this interplay between mathematics and software engineering yields results that are mathematically interesting, conceptually revealing, and practically useful. The theory presented by the authors has its origins in work on algebraic specifications that started in the early 1970s, and their treatment is comprehensive. This book contains five kinds of material: the requisite mathematical foundations; traditional algebraic specifications; elements of the theory of institutions; formal specification and development; and proof methods. While the book is self-contained, mathematical maturity and familiarity with the problems of software engineering is required; and in the examples that directly relate to programming, the authors assume acquaintance with the concepts of functional programming. The book will be of value to researchers and advanced graduate students in the areas of programming and theoretical computer science.
Book Synopsis Proceedings by : Clifford H. Bergman
Download or read book Proceedings written by Clifford H. Bergman and published by . This book was released on 1990 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Category Theory for Computing Science by : Michael Barr
Download or read book Category Theory for Computing Science written by Michael Barr and published by . This book was released on 1995 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: A wide coverage of topics in category theory and computer science is developed in this text, including introductory treatments of cartesian closed categories, sketches and elementary categorical model theory, and triples. Over 300 exercises are included.
Book Synopsis Universal Algebra by : Clifford Bergman
Download or read book Universal Algebra written by Clifford Bergman and published by CRC Press. This book was released on 2011-09-20 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
