Universal Algebra For Computer Scientists

Author : Wolfgang Wechler
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 50,6 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642767715

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Universal Algebra for Computer Scientists by Wolfgang Wechler Pdf

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 : Klaus Denecke,Shelly L. Wismath
Publisher : CRC Press
Page : 396 pages
File Size : 49,6 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9781482285833

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Universal Algebra and Applications in Theoretical Computer Science by Klaus Denecke,Shelly L. Wismath Pdf

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 : Janusz Czelakowski
Publisher : Springer
Page : 454 pages
File Size : 49,5 Mb
Release : 2018-03-20
Category : Philosophy
ISBN : 9783319747729

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Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science by Janusz Czelakowski Pdf

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.

Author : Klaus Denecke,Shelly L. Wismath
Publisher : World Scientific
Page : 291 pages
File Size : 55,9 Mb
Release : 2009
Category : Mathematics
ISBN : 9789812837455

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Universal Algebra and Coalgebra by Klaus Denecke,Shelly L. Wismath Pdf

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 H. Bergman,Roger D. Maddux,Don L. Pigozzi
Publisher : Springer
Page : 292 pages
File Size : 50,6 Mb
Release : 2000-11-13
Category : Computers
ISBN : 0387972889

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Algebraic Logic and Universal Algebra in Computer Science by Clifford H. Bergman,Roger D. Maddux,Don L. Pigozzi Pdf

Author : United States. Securities and Exchange Commission
Publisher : Unknown
Page : 300 pages
File Size : 41,9 Mb
Release : 1988
Category : Securities
ISBN : MINN:30000007281623

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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 Pdf

Author : Clifford H. Bergman
Publisher : Unknown
Page : 292 pages
File Size : 45,7 Mb
Release : 1990
Category : Electronic
ISBN : OCLC:658622946

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Algebraic Logic and Universal Algebra in Computer Science by Clifford H. Bergman Pdf

Author : Eric Lehman,F. Thomson Leighton,Albert R. Meyer
Publisher : Unknown
Page : 988 pages
File Size : 46,9 Mb
Release : 2017-03-08
Category : Business & Economics
ISBN : 9888407066

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Mathematics for Computer Science by Eric Lehman,F. Thomson Leighton,Albert R. Meyer Pdf

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.

Author : George Grätzer
Publisher : Springer Science & Business Media
Page : 601 pages
File Size : 48,8 Mb
Release : 2008-12-15
Category : Mathematics
ISBN : 9780387774879

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Universal Algebra by George Grätzer Pdf

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 : Benjamin C. Pierce
Publisher : MIT Press
Page : 117 pages
File Size : 51,7 Mb
Release : 1991-08-07
Category : Computers
ISBN : 9780262326452

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Basic Category Theory for Computer Scientists by Benjamin C. Pierce Pdf

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

Author : S. Burris,H. P. Sankappanavar
Publisher : Springer
Page : 276 pages
File Size : 42,6 Mb
Release : 2011-10-21
Category : Mathematics
ISBN : 1461381320

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A Course in Universal Algebra by S. Burris,H. P. Sankappanavar Pdf

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.

Author : Uli Fahrenberg,Mai Gehrke,Luigi Santocanale,Michael Winter
Publisher : Springer Nature
Page : 515 pages
File Size : 51,8 Mb
Release : 2021-10-22
Category : Computers
ISBN : 9783030887018

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Relational and Algebraic Methods in Computer Science by Uli Fahrenberg,Mai Gehrke,Luigi Santocanale,Michael Winter Pdf

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.

Author : Jorge Almeida
Publisher : World Scientific
Page : 532 pages
File Size : 55,7 Mb
Release : 1995-01-27
Category : Mathematics
ISBN : 9789814501569

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Finite Semigroups and Universal Algebra by Jorge Almeida Pdf

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

Author : Benjamin C. Pierce
Publisher : MIT Press
Page : 126 pages
File Size : 46,5 Mb
Release : 1991-08-07
Category : Computers
ISBN : 0262660717

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Basic Category Theory for Computer Scientists by Benjamin C. Pierce Pdf

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

Author : Ivo G. Rosenberg,Gert Sabidussi
Publisher : Springer Science & Business Media
Page : 565 pages
File Size : 41,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401706971

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Algebras and Orders by Ivo G. Rosenberg,Gert Sabidussi Pdf

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.