Introduction to lattice theory with computer science applications / (Record no. 12171)
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| 010 ## - LIBRARY OF CONGRESS CONTROL NUMBER | |
| LC control number | 2015007773 |
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| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781119069713 |
| Qualifying information | (electronic bk.) |
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| International Standard Book Number | 1119069718 |
| Qualifying information | (electronic bk.) |
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| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
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| 037 ## - SOURCE OF ACQUISITION | |
| Stock number | CL0500000671 |
| Source of stock number/acquisition | Safari Books Online |
| 042 ## - AUTHENTICATION CODE | |
| Authentication code | pcc |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA76.9.L38 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | COM |
| Subject category code subdivision | 013000 |
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| Subject category code | COM |
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| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 004.01/51 |
| Edition number | 23 |
| 049 ## - LOCAL HOLDINGS (OCLC) | |
| Holding library | MAIN |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Garg, Vijay K. |
| Fuller form of name | (Vijay Kumar), |
| Dates associated with a name | 1963- |
| 245 10 - TITLE STATEMENT | |
| Title | Introduction to lattice theory with computer science applications / |
| Statement of responsibility, etc. | Vijay K. Garg. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Hoboken, New Jersey : |
| Name of producer, publisher, distributor, manufacturer | Wiley, |
| Date of production, publication, distribution, manufacture, or copyright notice | [2015] |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | �2015 |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
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| 337 ## - MEDIA TYPE | |
| Media type term | computer |
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| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
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| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc. note | Includes bibliographical references and index. |
| 588 0# - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Print version record and CIP data provided by publisher. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | 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. |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover; Table of Contents; Title Page; Copyright; Dedication; List Of Figures; Nomenclature; Preface; Chapter 1: Introduction; 1.1 Introduction; 1.2 Relations; 1.3 Partial Orders; 1.4 Join and Meet Operations; 1.5 Operations on Posets; 1.6 Ideals and Filters; 1.7 Special Elements in Posets; 1.8 Irreducible Elements; 1.9 Dissector Elements; 1.10 Applications: Distributed Computations; 1.11 Applications: Combinatorics; 1.12 Notation and Proof Format; 1.13 Problems; 1.14 Bibliographic Remarks; Chapter 2: Representing Posets; 2.1 Introduction; 2.2 Labeling Elements of The Poset. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 2.3 Adjacency List Representation2.4 Vector Clock Representation; 2.5 Matrix Representation; 2.6 Dimension-Based Representation; 2.7 Algorithms to Compute Irreducibles; 2.8 Infinite Posets; 2.9 Problems; 2.10 Bibliographic Remarks; Chapter 3: Dilworth's Theorem; 3.1 Introduction; 3.2 Dilworth's Theorem; 3.3 Appreciation of Dilworth's Theorem; 3.4 Dual of Dilworth's Theorem; 3.5 Generalizations of Dilworth's Theorem; 3.6 Algorithmic Perspective of Dilworth's Theorem; 3.7 Application: Hall's Marriage Theorem; 3.8 Application: Bipartite Matching; 3.9 Online Decomposition of posets. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 3.10 A Lower Bound on Online Chain Partition3.11 Problems; 3.12 Bibliographic Remarks; Chapter 4: Merging Algorithms; 4.1 Introduction; 4.2 Algorithm to Merge Chains in Vector Clock Representation; 4.3 An Upper Bound for Detecting an Antichain of Size; 4.4 A Lower Bound for Detecting an Antichain of Size; 4.5 An Incremental Algorithm for Optimal Chain Decomposition; 4.6 Problems; 4.7 Bibliographic Remarks; Chapter 5: Lattices; 5.1 Introduction; 5.2 Sublattices; 5.3 Lattices as Algebraic Structures; 5.4 Bounding The Size of The Cover Relation of a Lattice. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 5.5 Join-Irreducible Elements Revisited5.6 Problems; 5.7 Bibliographic Remarks; Chapter 6: Lattice Completion; 6.1 INTRODUCTION; 6.2 COMPLETE LATTICES; 6.3 CLOSURE OPERATORS; 6.4 TOPPED -STRUCTURES; 6.5 DEDEKIND-MACNEILLE COMPLETION; 6.6 STRUCTURE OF DEDEKIND-MACNEILLE COMPLETION OF A POSET; 6.7 AN INCREMENTAL ALGORITHM FOR LATTICE COMPLETION; 6.8 BREADTH FIRST SEARCH ENUMERATION OF NORMAL CUTS; 6.9 DEPTH FIRST SEARCH ENUMERATION OF NORMAL CUTS; 6.10 APPLICATION: FINDING THE MEET AND JOIN OF EVENTS; 6.11 APPLICATION: DETECTING GLOBAL PREDICATES IN DISTRIBUTED SYSTEMS. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 6.12 APPLICATION: DATA MINING6.13 PROBLEMS; 6.14 BIBLIOGRAPHIC REMARKS; Chapter 7: Morphisms; 7.1 INTRODUCTION; 7.2 LATTICE HOMOMORPHISM; 7.3 LATTICE ISOMORPHISM; 7.4 LATTICE CONGRUENCES; 7.5 QUOTIENT LATTICE; 7.6 LATTICE HOMOMORPHISM AND CONGRUENCE; 7.7 PROPERTIES OF LATTICE CONGRUENCE BLOCKS; 7.8 APPLICATION: MODEL CHECKING ON REDUCED LATTICES; 7.9 PROBLEMS; 7.10 BIBLIOGRAPHIC REMARKS; Chapter 8: Modular Lattices; 8.1 INTRODUCTION; 8.2 MODULAR LATTICE; 8.3 CHARACTERIZATION OF MODULAR LATTICES; 8.4 PROBLEMS; 8.5 BIBLIOGRAPHIC REMARKS; Chapter 9: Distributive Lattices; 9.1 INTRODUCTION. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | John Wiley and Sons |
| Provenance (VM) [OBSOLETE] | Wiley Online Library: Complete oBooks |
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| Topical term or geographic name entry element | Lattice theory |
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| Relationship information | has work: |
| Label | Introduction to lattice theory with computer science applications (Text) |
| Real World Object URI | https://id.oclc.org/worldcat/entity/E39PCFHBpJtfrmPm9F9MKjMHG3 |
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| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Garg, Vijay K. (Vijay Kumar), 1963- |
| Title | Introduction to lattice theory with computer science applications. |
| Place, publisher, and date of publication | Hoboken, New Jersey : John Wiley & Sons, Inc., [2015] |
| International Standard Book Number | 9781118914373 |
| Record control number | (DLC) 2015003602 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://onlinelibrary.wiley.com/doi/book/10.1002/9781119069706">https://onlinelibrary.wiley.com/doi/book/10.1002/9781119069706</a> |
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