LEADER 05854nam 2200805z 450 001 9910877345803321 005 20230830174931.0 010 $a9781119069713 010 $a1119069718 010 $a9781119069737 010 $a1119069734 010 $a9781119069706 010 $a111906970X 035 $a(CKB)3710000000440580 035 $a(EBL)1895351 035 $a(SSID)ssj0001516333 035 $a(PQKBManifestationID)12644524 035 $a(PQKBTitleCode)TC0001516333 035 $a(PQKBWorkID)11494926 035 $a(PQKB)11330004 035 $a(PQKBManifestationID)16037382 035 $a(PQKB)21187855 035 $a(MiAaPQ)EBC4040924 035 $a(DLC) 2015007773 035 $a(MiAaPQ)EBC1895351 035 $a(Au-PeEL)EBL1895351 035 $a(OCoLC)904047561 035 $a(CaSebORM)9781118914373 035 $a(JP-MeL)3000111741 035 $a(NjHacI)993710000000440580 035 $a(PPN)190985720 035 $a(OCoLC)928712410 035 $a(OCoLC)ocn928712410 035 $a(EXLCZ)993710000000440580 100 $a20220914d ||| || 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aIntroduction to lattice theory with computer science applications /$fVijay K. Garg 205 $a1st edition 210 $aHoboken, N.J.$cWiley$dc2015 210 1$aHoboken, N.J. :$cWiley,$d2015. 215 $a1 online resource (494 p.) 300 $aIncludes bibliographical references and index 311 08$a9781118914373 311 08$a1118914376 320 $aIncludes bibliographical references (pages 229-233) and index. 327 $aCover; 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 327 $a2.3 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 327 $a3.10 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 327 $a5.5 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 327 $a6.12 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 327 $a9.2 FORBIDDEN SUBLATTICES 330 $aA 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 606 $6880-03/$1$aComputer science -- Mathematics 606 $6880-04/$1$aEngineering mathematics 606 $6880-05/$1$aLattice theory 615 0$aComputer science -- Mathematics 615 0$aEngineering mathematics 615 0$aLattice theory 676 $a004.01/51 686 $a007$2njb/09 686 $a004.01/51$2njb/09 700 $aGarg$b Vijay K$g(Vijay Kumar),$f1963-$0845526 801 1$bJP-MeL 906 $aBOOK 912 $a9910877345803321 996 $aIntroduction to lattice theory with computer science applications$94304280 997 $aUNINA