Introduction To Lattice Theory With Computer Science Applications
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Introduction To Lattice Theory With Computer Science Applications
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Author : Vijay K. Garg
language : en
Publisher: John Wiley & Sons
Release Date : 2016-03-02
Introduction To Lattice Theory With Computer Science Applications written by Vijay K. Garg and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Computers categories.
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
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Author : Gerhard X. Ritter
language : en
Publisher: CRC Press
Release Date : 2021-08-23
Introduction To Lattice Algebra written by Gerhard X. Ritter and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-23 with Mathematics categories.
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.
Introduction To Lattices And Order
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Author : B. A. Davey
language : en
Publisher:
Release Date : 1990
Introduction To Lattices And Order written by B. A. Davey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
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.
Lattice Basis Reduction
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Author : Murray R. Bremner
language : en
Publisher: CRC Press
Release Date : 2011-08-12
Lattice Basis Reduction written by Murray R. Bremner and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-12 with Computers categories.
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
Semigroups In Complete Lattices
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Author : Patrik Eklund
language : en
Publisher: Springer
Release Date : 2018-06-09
Semigroups In Complete Lattices written by Patrik Eklund and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-09 with Mathematics categories.
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.
Computer Science And Multiple Valued Logic
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Author : David C. Rine
language : en
Publisher: Elsevier
Release Date : 2014-05-12
Computer Science And Multiple Valued Logic written by David C. Rine and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Technology & Engineering categories.
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.
Complexity Of Lattice Problems
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Author : Daniele Micciancio
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Complexity Of Lattice Problems written by Daniele Micciancio and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
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.
Lattices And Ordered Sets
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Author : Steven Roman
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-15
Lattices And Ordered Sets written by Steven Roman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-15 with Mathematics categories.
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.
Topological Duality For Distributive Lattices
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Author : Mai Gehrke
language : en
Publisher: Cambridge University Press
Release Date : 2024-02-29
Topological Duality For Distributive Lattices written by Mai Gehrke and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-29 with Computers categories.
Introducing Stone–Priestley duality theory and its applications to logic and theoretical computer science, this book equips graduate students and researchers with the theoretical background necessary for reading and understanding current research in the area. After giving a thorough introduction to the algebraic, topological, logical, and categorical aspects of the theory, the book covers two advanced applications in computer science, namely in domain theory and automata theory. These topics are at the forefront of active research seeking to unify semantic methods with more algorithmic topics in finite model theory. Frequent exercises punctuate the text, with hints and references provided.
Mathematical Foundation Of Computer Science
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Author : Y. N. Singh
language : en
Publisher: New Age International
Release Date : 2005
Mathematical Foundation Of Computer Science written by Y. N. Singh and has been published by New Age International this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
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.