Universal Algebra And Applications In Theoretical Computer Science

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Universal Algebra and Applications in Theoretical Computer Science

Klaus Denecke,Shelly L. Wismath
Universal Algebra and Applications in Theoretical Computer Science Book PDF

Author : Klaus Denecke,Shelly L. Wismath
Publisher : CRC Press
Page : 396 pages
File Size : 42,8 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.

Universal Algebra for Computer Scientists

Wolfgang Wechler
Universal Algebra for Computer Scientists Book PDF

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.

Algebra and Computer Science

Delaram Kahrobaei,Bren Cavallo,David Garber
Algebra and Computer Science Book PDF

Author : Delaram Kahrobaei,Bren Cavallo,David Garber
Publisher : American Mathematical Soc.
Page : 229 pages
File Size : 45,7 Mb
Release : 2016-11-28
Category : Algebra
ISBN : 9781470423032

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Algebra and Computer Science by Delaram Kahrobaei,Bren Cavallo,David Garber Pdf

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.

Basic Category Theory for Computer Scientists

Benjamin C. Pierce
Basic Category Theory for Computer Scientists Book PDF

Author : Benjamin C. Pierce
Publisher : MIT Press
Page : 126 pages
File Size : 46,7 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

Universal Algebra and Coalgebra

Klaus Denecke,Shelly L. Wismath
Universal Algebra and Coalgebra Book PDF

Author : Klaus Denecke,Shelly L. Wismath
Publisher : World Scientific
Page : 291 pages
File Size : 41,8 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.

Handbook of Logic in Computer Science

S. Abramsky,Dov M. Gabbay,Thomas S. E. Maibaum
Handbook of Logic in Computer Science Book PDF

Author : S. Abramsky,Dov M. Gabbay,Thomas S. E. Maibaum
Publisher : Unknown
Page : 0 pages
File Size : 46,6 Mb
Release : 2023
Category : Computer science
ISBN : 1383026025

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Handbook of Logic in Computer Science by S. Abramsky,Dov M. Gabbay,Thomas S. E. Maibaum Pdf

Part of a multi-volume work that has been designed to cover all major areas of the application of logic to theoretical computer science, this book explores valuation systems, recursion theory, universal algebra, basic category theory, topology and model theory.

Mathematical Logic and Theoretical Computer Science

Kueker
Mathematical Logic and Theoretical Computer Science Book PDF

Author : Kueker
Publisher : CRC Press
Page : 420 pages
File Size : 40,9 Mb
Release : 1986-12-22
Category : Mathematics
ISBN : 0824777468

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Mathematical Logic and Theoretical Computer Science by Kueker Pdf

This book includes articles on denotational semanitcs, recursion theoretic aspects of computer science, model theory and algebra, automath and automated reasoning, stability theory, topoi and mathematics, and topoi and logic. It is intended for mathematical logicians and computer scientists.

Structural Theory of Automata, Semigroups, and Universal Algebra

Valery B. Kudryavtsev,Ivo G. Rosenberg
Structural Theory of Automata Semigroups and Universal Algebra Book PDF

Author : Valery B. Kudryavtsev,Ivo G. Rosenberg
Publisher : Springer Science & Business Media
Page : 448 pages
File Size : 43,5 Mb
Release : 2006-01-18
Category : Mathematics
ISBN : 9781402038174

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Structural Theory of Automata, Semigroups, and Universal Algebra by Valery B. Kudryavtsev,Ivo G. Rosenberg Pdf

Semigroups, Automata, Universal Algebra, Varieties

Finite Semigroups and Universal Algebra

Jorge Almeida
Finite Semigroups and Universal Algebra Book PDF

Author : Jorge Almeida
Publisher : World Scientific
Page : 532 pages
File Size : 53,7 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

A Course in Universal Algebra

S. Burris,H. P. Sankappanavar
A Course in Universal Algebra Book PDF

Author : S. Burris,H. P. Sankappanavar
Publisher : Springer
Page : 276 pages
File Size : 44,6 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.

Algebra for Computer Science

Lars Garding,Torbjörn Tambour
Algebra for Computer Science Book PDF

Author : Lars Garding,Torbjörn Tambour
Publisher : Springer
Page : 214 pages
File Size : 50,6 Mb
Release : 1988-08
Category : Computers
ISBN : UOM:39015013840049

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Algebra for Computer Science by Lars Garding,Torbjörn Tambour Pdf

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, .

FST TCS 2003: Foundations of Software Technology and Theoretical Computer Science

Paritosh K Pandya
FST TCS 2003 Foundations of Software Technology and Theoretical Computer Science Book PDF

Author : Paritosh K Pandya
Publisher : Springer Science & Business Media
Page : 457 pages
File Size : 51,7 Mb
Release : 2003-12-03
Category : Computers
ISBN : 9783540206804

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FST TCS 2003: Foundations of Software Technology and Theoretical Computer Science by Paritosh K Pandya Pdf

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.

Universal Algebra, Algebraic Logic, and Databases

B. Plotkin
Universal Algebra Algebraic Logic and Databases Book PDF

Author : B. Plotkin
Publisher : Springer Science & Business Media
Page : 445 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401108201

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Universal Algebra, Algebraic Logic, and Databases by B. Plotkin Pdf

Modern algebra, which not long ago seemed to be a science divorced from real life, now has numerous applications. Many fine algebraic structures are endowed with meaningful contents. Now and then practice suggests new and unexpected structures enriching algebra. This does not mean that algebra has become merely a tool for applications. Quite the contrary, it significantly benefits from the new connections. The present book is devoted to some algebraic aspects of the theory of databases. It consists of three parts. The first part contains information about universal algebra, algebraic logic is the subject of the second part, and the third one deals with databases. The algebraic material of the flI'St two parts serves the common purpose of applying algebra to databases. The book is intended for use by mathematicians, and mainly by algebraists, who realize the necessity to unite theory and practice. It is also addressed to programmers, engineers and all potential users of mathematics who want to construct their models with the help of algebra and logic. Nowadays, the majority of professional mathematicians work in close cooperation with representatives of applied sciences and even industrial technology. It is neces sary to develop an ability to see mathematics in different particular situations. One of the tasks of this book is to promote the acquisition of such skills.

Category Theory And Applications: A Textbook For Beginners (Second Edition)

Marco Grandis
Category Theory And Applications A Textbook For Beginners Second Edition Book PDF

Author : Marco Grandis
Publisher : World Scientific
Page : 390 pages
File Size : 40,8 Mb
Release : 2021-03-05
Category : Mathematics
ISBN : 9789811236105

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Category Theory And Applications: A Textbook For Beginners (Second Edition) by Marco Grandis Pdf

Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a better understanding of their roots.This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers the basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications.A reader should have some elementary knowledge of these three subjects, or at least two of them, in order to be able to follow the main examples, appreciate the unifying power of the categorical approach, and discover the subterranean links brought to light and formalised by this perspective.Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications in Algebra and Topology, with a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields.In this second edition, the book has been entirely reviewed, adding many applications and exercises. All non-obvious exercises have now a solution (or a reference, in the case of an advanced topic); solutions are now collected in the last chapter.

Algebra and Coalgebra in Computer Science

Alexander Kurz,Marina Lenisa
Algebra and Coalgebra in Computer Science Book PDF

Author : Alexander Kurz,Marina Lenisa
Publisher : Springer
Page : 457 pages
File Size : 52,7 Mb
Release : 2009-09-19
Category : Computers
ISBN : 9783642037412

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Algebra and Coalgebra in Computer Science by Alexander Kurz,Marina Lenisa Pdf

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.