Introduction To Lattice Theory With Computer Science Applications

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Introduction to Lattice Theory with Computer Science Applications

Vijay K. Garg
Introduction to Lattice Theory with Computer Science Applications Book PDF

Author : Vijay K. Garg
Publisher : John Wiley & Sons
Page : 272 pages
File Size : 40,5 Mb
Release : 2016-03-02
Category : Computers
ISBN : 9781119069737

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Introduction to Lattice Theory with Computer Science Applications by Vijay K. Garg Pdf

A computational perspective on partial order and lattice theory, focusing on algorithms and their applications This book provides a uniform treatment of the theory and applications of lattice theory. The applications covered include tracking dependency in distributed systems, combinatorics, detecting global predicates in distributed systems, set families, and integer partitions. The book presents algorithmic proofs of theorems whenever possible. These proofs are written in the calculational style advocated by Dijkstra, with arguments explicitly spelled out step by step. The author’s intent is for readers to learn not only the proofs, but the heuristics that guide said proofs. Introduction to Lattice Theory with Computer Science Applications: Examines; posets, Dilworth’s theorem, merging algorithms, lattices, lattice completion, morphisms, modular and distributive lattices, slicing, interval orders, tractable posets, lattice enumeration algorithms, and dimension theory Provides end of chapter exercises to help readers retain newfound knowledge on each subject Includes supplementary material at www.ece.utexas.edu/~garg Introduction to Lattice Theory with Computer Science Applications is written for students of computer science, as well as practicing mathematicians.

Introduction to Lattice Algebra

Gerhard X. Ritter,Gonzalo Urcid
Introduction to Lattice Algebra Book PDF

Author : Gerhard X. Ritter,Gonzalo Urcid
Publisher : CRC Press
Page : 292 pages
File Size : 46,9 Mb
Release : 2021-08-23
Category : Mathematics
ISBN : 9781000412604

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Introduction to Lattice Algebra by Gerhard X. Ritter,Gonzalo Urcid Pdf

Lattice theory extends into virtually every branch of mathematics, ranging from measure theory and convex geometry to probability theory and topology. A more recent development has been the rapid escalation of employing lattice theory for various applications outside the domain of pure mathematics. These applications range from electronic communication theory and gate array devices that implement Boolean logic to artificial intelligence and computer science in general. Introduction to Lattice Algebra: With Applications in AI, Pattern Recognition, Image Analysis, and Biomimetic Neural Networks lays emphasis on two subjects, the first being lattice algebra and the second the practical applications of that algebra. This textbook is intended to be used for a special topics course in artificial intelligence with a focus on pattern recognition, multispectral image analysis, and biomimetic artificial neural networks. The book is self-contained and – depending on the student’s major – can be used for a senior undergraduate level or first-year graduate level course. The book is also an ideal self-study guide for researchers and professionals in the above-mentioned disciplines. Features Filled with instructive examples and exercises to help build understanding Suitable for researchers, professionals and students, both in mathematics and computer science Contains numerous exercises.

Lattice Basis Reduction

Murray R. Bremner
Lattice Basis Reduction Book PDF

Author : Murray R. Bremner
Publisher : CRC Press
Page : 330 pages
File Size : 55,8 Mb
Release : 2011-08-12
Category : Computers
ISBN : 9781439807040

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Lattice Basis Reduction by Murray R. Bremner Pdf

First developed in the early 1980s by Lenstra, Lenstra, and Lovasz, the LLL algorithm was originally used to provide a polynomial-time algorithm for factoring polynomials with rational coefficients. It very quickly became an essential tool in integer linear programming problems and was later adapted for use in cryptanalysis. This book provides an i

Introduction to Lattices and Order

B. A. Davey,H. A. Priestley
Introduction to Lattices and Order Book PDF

Author : B. A. Davey,H. A. Priestley
Publisher : Cambridge University Press
Page : 316 pages
File Size : 54,8 Mb
Release : 2002-04-18
Category : Mathematics
ISBN : 0521784514

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Introduction to Lattices and Order by B. A. Davey,H. A. Priestley Pdf

This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures.

Recent Advances in Applications of Computational and Fuzzy Mathematics

Snehashish Chakraverty,Sanjeewa Perera
Recent Advances in Applications of Computational and Fuzzy Mathematics Book PDF

Author : Snehashish Chakraverty,Sanjeewa Perera
Publisher : Springer
Page : 178 pages
File Size : 47,7 Mb
Release : 2018-07-17
Category : Computers
ISBN : 9789811311536

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Recent Advances in Applications of Computational and Fuzzy Mathematics by Snehashish Chakraverty,Sanjeewa Perera Pdf

This book addresses the basics of interval/fuzzy set theory, artificial neural networks (ANN) and computational methods. It presents step-by-step modeling for application problems along with simulation and numerical solutions. In general, every science and engineering problem is inherently biased by uncertainty, and there is often a need to model, solve and interpret problems in the world of uncertainty. At the same time, exact information about models and parameters of practical applications is usually not known and precise values do not exist. This book discusses uncertainty in both data and models. It consists of seven chapters covering various aspects of fuzzy uncertainty in application problems, such as shallow water wave equations, static structural problems, robotics, radon diffusion in soil, risk of invasive alien species and air quality quantification. These problems are handled by means of advanced computational and fuzzy theory along with machine intelligence when the uncertainties involved are fuzzy. The proposed computational methods offer new fuzzy computing methods that help other areas of knowledge construction where inexact information is present.

Introduction to Lattices and Order

B. A. Davey,Hilary A. Priestley
Introduction to Lattices and Order Book PDF

Author : B. A. Davey,Hilary A. Priestley
Publisher : Unknown
Page : 248 pages
File Size : 42,5 Mb
Release : 1990
Category : Mathematics
ISBN : 0521365848

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Introduction to Lattices and Order by B. A. Davey,Hilary A. Priestley Pdf

This is the first introductory textbook on ordered sets and lattices, and covers both the basic theory and its applications. The importance of ordered structures has been increasingly recognised in recent years due to an explosion of interest in computer science and all areas of discrete mathematics. The authors provide a thorough introduction to ordered sets, lattices, distributive lattices and Boolean algebras. Ordered sets, and in particular lattices, can be represented pictorially, and this key feature is emphasised throughout. Lattices are also considered as algebraic structures and their study from this viewpoint reinforces ideas encountered in the theory of groups and rings. The representation of distributive lattices by ordered topological spaces is presented; a self-contained treatment of the requisite topology is included. Two chapters are devoted to topics with application to computer science. These cover complete partial orders, domains (including their relation to information systems), and fixpoint theory. Another chapter deals with formal concept analysis - a new and important application of lattice theory of interest to mathematicians and social scientists. Prerequisites are minimal; all that is assumed is exposure to the notation of set theory and elementary abstract algebra. The numerous classroom-tested exercises will make the book especially useful for course accompaniment, but it will also be valuable as a background reference for mathematicians, logicians and computer scientists.

Complexity of Lattice Problems

Daniele Micciancio,Shafi Goldwasser
Complexity of Lattice Problems Book PDF

Author : Daniele Micciancio,Shafi Goldwasser
Publisher : Springer Science & Business Media
Page : 229 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461508977

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Complexity of Lattice Problems by Daniele Micciancio,Shafi Goldwasser Pdf

Lattices are geometric objects that can be pictorially described as the set of intersection points of an infinite, regular n-dimensional grid. De spite their apparent simplicity, lattices hide a rich combinatorial struc ture, which has attracted the attention of great mathematicians over the last two centuries. Not surprisingly, lattices have found numerous ap plications in mathematics and computer science, ranging from number theory and Diophantine approximation, to combinatorial optimization and cryptography. The study of lattices, specifically from a computational point of view, was marked by two major breakthroughs: the development of the LLL lattice reduction algorithm by Lenstra, Lenstra and Lovasz in the early 80's, and Ajtai's discovery of a connection between the worst-case and average-case hardness of certain lattice problems in the late 90's. The LLL algorithm, despite the relatively poor quality of the solution it gives in the worst case, allowed to devise polynomial time solutions to many classical problems in computer science. These include, solving integer programs in a fixed number of variables, factoring polynomials over the rationals, breaking knapsack based cryptosystems, and finding solutions to many other Diophantine and cryptanalysis problems.

Graph-Based Representation and Reasoning

Manuel Ojeda-Aciego,Kai Sauerwald,Robert Jäschke
Graph Based Representation and Reasoning Book PDF

Author : Manuel Ojeda-Aciego,Kai Sauerwald,Robert Jäschke
Publisher : Springer Nature
Page : 213 pages
File Size : 53,8 Mb
Release : 2023-08-15
Category : Computers
ISBN : 9783031409608

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Graph-Based Representation and Reasoning by Manuel Ojeda-Aciego,Kai Sauerwald,Robert Jäschke Pdf

This book constitutes the refereed deadline proceedings of the 28th International Conference on Graph-Based Representation and Reasoning, ICCS 2023, held in Berlin, Germany, during September 11–13, 2023. The 9 full papers, 5 short papers and 4 Posters are included in this book were carefully reviewed and selected from 32 submissions. They were organized in topical sections as follows: Complexity and Database Theory, Formal Concept Analysis: Theoretical Advances, Formal Concept Analysis: Applications, Modelling and Explanation, Semantic Web and Graphs, Posters.

Computer Science and Multiple-Valued Logic

David C. Rine
Computer Science and Multiple Valued Logic Book PDF

Author : David C. Rine
Publisher : Elsevier
Page : 563 pages
File Size : 53,6 Mb
Release : 2014-05-12
Category : Technology & Engineering
ISBN : 9781483257921

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Computer Science and Multiple-Valued Logic by David C. Rine Pdf

Computer Science and Multiple-Valued Logic: Theory and Applications focuses on the processes, methodologies, and approaches involved in multiple-valued logic and its relationship to computer science. The selection first tackles an introduction to multiple-valued logic, lattice theory of post algebras, multiple-valued logic design and applications in binary computers, smallest many-valued logic for the treatment of complemented and uncomplemented error signals, and chain based lattices. Discussions focus on formulation, representation theory, theory and circuit design, logical tables, and unary operations. The text then examines multiple-valued signal processing with limiting, development of multiple-valued logic as related to computer science, p-algebras, and an algorithm for axiomatizing every finite logic. The book takes a look at completeness properties of multiple-valued logic algebras, computer simplification of multi-valued switching functions, and minimization of multivalued functions. Topics include generation of prime implicants, realizations, minimization algorithms, decomposition algorithm for multi-valued switching functions, and relation between the sum-of-products form and array of cubes. The selection is aimed at computer engineers, computer scientists, applied mathematicians, and physicists interested in multiple-valued logic as the discipline relates to computer engineering and computer science.

Semigroups in Complete Lattices

Patrik Eklund,Javier Gutiérrez García,Ulrich Höhle,Jari Kortelainen
Semigroups in Complete Lattices Book PDF

Author : Patrik Eklund,Javier Gutiérrez García,Ulrich Höhle,Jari Kortelainen
Publisher : Springer
Page : 326 pages
File Size : 44,8 Mb
Release : 2018-06-09
Category : Mathematics
ISBN : 9783319789484

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Semigroups in Complete Lattices by Patrik Eklund,Javier Gutiérrez García,Ulrich Höhle,Jari Kortelainen Pdf

This monograph provides a modern introduction to the theory of quantales. First coined by C.J. Mulvey in 1986, quantales have since developed into a significant topic at the crossroads of algebra and logic, of notable interest to theoretical computer science. This book recasts the subject within the powerful framework of categorical algebra, showcasing its versatility through applications to C*- and MV-algebras, fuzzy sets and automata. With exercises and historical remarks at the end of each chapter, this self-contained book provides readers with a valuable source of references and hints for future research. This book will appeal to researchers across mathematics and computer science with an interest in category theory, lattice theory, and many-valued logic.

Lattices and Ordered Sets

Steven Roman
Lattices and Ordered Sets Book PDF

Author : Steven Roman
Publisher : Springer Science & Business Media
Page : 307 pages
File Size : 47,7 Mb
Release : 2008-12-15
Category : Mathematics
ISBN : 9780387789019

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Lattices and Ordered Sets by Steven Roman Pdf

This book is intended to be a thorough introduction to the subject of order and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study. Prerequisites are kept to a minimum, but an introductory course in abstract algebra is highly recommended, since many of the examples are drawn from this area. This is a book on pure mathematics: I do not discuss the applications of lattice theory to physics, computer science or other disciplines. Lattice theory began in the early 1890s, when Richard Dedekind wanted to know the answer to the following question: Given three subgroups EF , and G of an abelian group K, what is the largest number of distinct subgroups that can be formed using these subgroups and the operations of intersection and sum (join), as in E?FßÐE?FÑ?GßE?ÐF?GÑ and so on? In lattice-theoretic terms, this is the number of elements in the relatively free modular lattice on three generators. Dedekind [15] answered this question (the answer is #)) and wrote two papers on the subject of lattice theory, but then the subject lay relatively dormant until Garrett Birkhoff, Oystein Ore and others picked it up in the 1930s. Since then, many noted mathematicians have contributed to the subject, including Garrett Birkhoff, Richard Dedekind, Israel Gelfand, George Grätzer, Aleksandr Kurosh, Anatoly Malcev, Oystein Ore, Gian-Carlo Rota, Alfred Tarski and Johnny von Neumann.

Semirings

Udo Hebisch,Hanns Joachim Weinert
Semirings Book PDF

Author : Udo Hebisch,Hanns Joachim Weinert
Publisher : World Scientific
Page : 382 pages
File Size : 43,9 Mb
Release : 1998
Category : Mathematics
ISBN : 9810236018

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Semirings by Udo Hebisch,Hanns Joachim Weinert Pdf

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.

Mathematical Foundation of Computer Science

Y. N. Singh
Mathematical Foundation of Computer Science Book PDF

Author : Y. N. Singh
Publisher : New Age International
Page : 24 pages
File Size : 53,5 Mb
Release : 2005
Category : Mathematics
ISBN : 9788122416671

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Mathematical Foundation of Computer Science by Y. N. Singh Pdf

The Interesting Feature Of This Book Is Its Organization And Structure. That Consists Of Systematizing Of The Definitions, Methods, And Results That Something Resembling A Theory. Simplicity, Clarity, And Precision Of Mathematical Language Makes Theoretical Topics More Appealing To The Readers Who Are Of Mathematical Or Non-Mathematical Background. For Quick References And Immediate Attentions3⁄4Concepts And Definitions, Methods And Theorems, And Key Notes Are Presented Through Highlighted Points From Beginning To End. Whenever, Necessary And Probable A Visual Approach Of Presentation Is Used. The Amalgamation Of Text And Figures Make Mathematical Rigors Easier To Understand. Each Chapter Begins With The Detailed Contents, Which Are Discussed Inside The Chapter And Conclude With A Summary Of The Material Covered In The Chapter. Summary Provides A Brief Overview Of All The Topics Covered In The Chapter. To Demonstrate The Principles Better, The Applicability Of The Concepts Discussed In Each Topic Are Illustrated By Several Examples Followed By The Practice Sets Or Exercises.

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 : 53,6 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.

The Mathematics of the Uncertain

Eduardo Gil,Eva Gil,Juan Gil,María Ángeles Gil
The Mathematics of the Uncertain Book PDF

Author : Eduardo Gil,Eva Gil,Juan Gil,María Ángeles Gil
Publisher : Springer
Page : 917 pages
File Size : 53,5 Mb
Release : 2018-02-28
Category : Technology & Engineering
ISBN : 9783319738482

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The Mathematics of the Uncertain by Eduardo Gil,Eva Gil,Juan Gil,María Ángeles Gil Pdf

This book is a tribute to Professor Pedro Gil, who created the Department of Statistics, OR and TM at the University of Oviedo, and a former President of the Spanish Society of Statistics and OR (SEIO). In more than eighty original contributions, it illustrates the extent to which Mathematics can help manage uncertainty, a factor that is inherent to real life. Today it goes without saying that, in order to model experiments and systems and to analyze related outcomes and data, it is necessary to consider formal ideas and develop scientific approaches and techniques for dealing with uncertainty. Mathematics is crucial in this endeavor, as this book demonstrates. As Professor Pedro Gil highlighted twenty years ago, there are several well-known mathematical branches for this purpose, including Mathematics of chance (Probability and Statistics), Mathematics of communication (Information Theory), and Mathematics of imprecision (Fuzzy Sets Theory and others). These branches often intertwine, since different sources of uncertainty can coexist, and they are not exhaustive. While most of the papers presented here address the three aforementioned fields, some hail from other Mathematical disciplines such as Operations Research; others, in turn, put the spotlight on real-world studies and applications. The intended audience of this book is mainly statisticians, mathematicians and computer scientists, but practitioners in these areas will certainly also find the book a very interesting read.