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Introduction to Lattice Theory with Computer Science Applications

2016-03-02 Computers
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Release : 2016-03-02
Genre : Computers
Kind : eBook
Book Rating : 734/5 ( reviews)

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Book Synopsis Introduction to Lattice Theory with Computer Science Applications by : Vijay K. Garg

Download or read book Introduction to Lattice Theory with Computer Science Applications written by Vijay K. Garg. This book was released on 2016-03-02. Available in PDF, EPUB and Kindle. Book excerpt: 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

2021-08-23 Mathematics
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Release : 2021-08-23
Genre : Mathematics
Kind : eBook
Book Rating : 601/5 ( reviews)

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Book Synopsis Introduction to Lattice Algebra by : Gerhard X. Ritter

Download or read book Introduction to Lattice Algebra written by Gerhard X. Ritter. This book was released on 2021-08-23. Available in PDF, EPUB and Kindle. Book excerpt: 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

2011-08-12 Computers
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Release : 2011-08-12
Genre : Computers
Kind : eBook
Book Rating : 043/5 ( reviews)

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Book Synopsis Lattice Basis Reduction by : Murray R. Bremner

Download or read book Lattice Basis Reduction written by Murray R. Bremner. This book was released on 2011-08-12. Available in PDF, EPUB and Kindle. Book excerpt: 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

Lattice Theory

2009-01-01 Mathematics
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Release : 2009-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 73X/5 ( reviews)

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Book Synopsis Lattice Theory by : George Gratzer

Download or read book Lattice Theory written by George Gratzer. This book was released on 2009-01-01. Available in PDF, EPUB and Kindle. Book excerpt: This outstanding text is written in clear language and enhanced with many exercises, diagrams, and proofs. It discusses historical developments and future directions and provides an extensive bibliography and references. 1971 edition.

Introduction to Lattices and Order

2002-04-18 Mathematics
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Release : 2002-04-18
Genre : Mathematics
Kind : eBook
Book Rating : 523/5 ( reviews)

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Book Synopsis Introduction to Lattices and Order by : B. A. Davey

Download or read book Introduction to Lattices and Order written by B. A. Davey. This book was released on 2002-04-18. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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