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عنوان
Introduction to lattice theory with computer science applications /

پدید آورنده
Vijay K. Garg

موضوع
Computer science-- Mathematics.,Engineering mathematics.,Lattice theory.

رده
QA76
.
9
.
L38

کتابخانه
کتابخانه مطالعات اسلامی به زبان های اروپایی

محل استقرار
استان: قم ـ شهر: قم

کتابخانه مطالعات اسلامی به زبان های اروپایی

تماس با کتابخانه : 32910706-025

1119069718
9781119069713
1118914376
111906970X
1119069734
9781118914373 (cloth)
9781119069706
9781119069737

dltt

Introduction to lattice theory with computer science applications /
[Book]
Vijay K. Garg

1 online resource

Includes bibliographical references and index

Introduction -- Introduction -- Relations -- Partial Orders -- Join and Meet Operations -- Operations on Posets -- Ideals and Filters -- Special Elements in Posets -- Irreducible Elements -- Dissector Elements -- Applications: Distributed Computations -- Applications: Combinatorics -- Notation and Proof Format -- Problems -- Bibliographic Remarks -- Representing Posets -- Introduction -- Labeling Elements of The Poset -- Adjacency List Representation -- Vector Clock Representation -- Matrix Representation -- Dimension-Based Representation -- Algorithms to Compute Irreducibles -- Infinite Posets -- Problems -- Bibliographic Remarks -- Dilworth's Theorem -- Introduction -- Dilworth's Theorem -- Appreciation of Dilworth's Theorem -- Dual of Dilworth's Theorem -- Generalizations of Dilworth's Theorem -- Algorithmic Perspective of Dilworth's Theorem -- Application: Hall's Marriage Theorem -- Application: Bipartite Matching -- Online Decomposition of Posets -- A Lower Bound on Online Chain Partition -- Problems -- Bibliographic Remarks -- Merging Algorithms -- Introduction -- Algorithm to Merge Chains in Vector Clock Representation -- An Upper Bound for Detecting an Aniichain of Size K -- A Lower Bound for Detecting an Antichain of Size K -- An Incremental Algorithm for Optimal Chain Decomposition -- Problems -- Bibliographic Remarks -- Lattices -- Introduction -- Sublattices -- Lattices as Algebraic Structures -- Bounding The Size of The Cover Relation of a Lattice -- Join-Irreducible Elements Revisited -- Problems -- Bibliographic Remarks -- Lattice Completion -- Introduction -- Complete Lattices -- Closure Operators -- Topped n-Structures -- Dedekind-Macneille Completion -- Structure of Dedekind-Macneille Completion of a Poset -- An Incremental Algorithm for Lattice Completion -- Breadth First Search Enumeration of Normal Cuts -- Depth First Search Enumeration of Normal Cuts -- Application: Finding the Meet and Join of Events -- Application: Detecting Global Predicates in Distributed Systems -- Application: Data Mining -- Problems -- Bibliographic Remarks -- Morphisms -- Introduction -- Lattice Homomorphism -- Lattice Isomorphism -- Lattice Congruences -- Quotient Lattice -- Lattice Homomorphism and Congruence -- Properties of Lattice Congruence Blocks -- Application: Model Checking on Reduced Lattices -- Problems -- Bibliographic Remarks -- Modular Lattices -- Introduction -- Modular Lattice -- Characterization of Modular Lattices -- Problems -- Bibliographic Remarks -- Distributive Lattices -- Introduction -- Forbidden Sublattices -- Join-Prime Elements -- Birkhoff's Representation Theorem -- Finitary Distributive Lattices -- Problems -- Bibliographic Remarks -- Slicing -- Introduction -- Representing Finite Distributive Lattices -- Predicates on Ideals -- Application: Slicing Distributed Computations -- Problems -- Bibliographic Remarks -- Applications of Slicing to Combinatorics -- Introduction -- Counting Ideals -- Boolean Algebra and Set Families -- Set Families of Size k -- Integer Partitions -- Permutations -- Problems -- Bibliographic Remarks -- Interval Orders -- Introduction -- Weak Order -- Semiorder -- Interval Order -- Problems -- Bibliographic Remarks -- Tractable Posets -- Introduction -- Series-Parallel Posets -- Two-Dimensional Posets -- Counting Ideals of a Two-Dimensional Poset -- Problems -- Bibliographic Remarks -- Enumeration Algorithms -- Introduction -- BFS Traversal -- DFS Traversal -- LEX Traversal -- Uniflow Partition of Posets -- Enumerating Tuples of Product Spaces -- Enumerating All Subsets -- Enumerating All Subsets of Size k -- Enumerating Young's Lattice -- Enumerating Permutations -- Lexical Enumeration of All Order Ideals of a Given Rank -- Problems -- Bibliographic Remarks -- Lattice of Maximal Antichains -- Introduction -- Maximal Antichain Lattice -- An Incremental Algorithm Based on Union Closure -- An Incremental Algorithm Based on BFS -- Traversal of the Lattice of Maximal Antichains -- Application: Detecting Antichain-Consistent Predicates -- Construction and Enumeration of Width Antichain Lattice -- Lexical Enumeration of Closed Sets -- Construction of Lattices Based on Union Closure -- Problems -- Bibliographic Remarks -- Dimension Theory -- Introduction -- Chain Realizers -- Standard Examples of Dimension Theory -- Relationship Between the Dimension and the Width of a Poset -- Removal Theorems for Dimension -- Critical Pairs in the Poset -- Rectangle Realizers -- Order Decomposition Method and Its Applications -- Problems -- Bibliographic Remarks -- Fixed Point Theory -- Complete Partial Orders -- Knaster-Tarski Theorem -- Application: Defining Recursion Using Fixed Points -- Problems -- Bibliographic Remarks
0

Safari Books Online
CL0500000671

Introduction to lattice theory with computer science applications
9781118914373

Computer science-- Mathematics.
Engineering mathematics.
Lattice theory.

COM-- 013000
COM-- 014000
COM-- 018000
COM-- 032000
COM-- 037000
COM-- 052000
COM-- 067000

004
.
01/51
23

QA76
.
9
.
L38

Garg, Vijay K., (Vijay Kumar),1963-

Ohio Library and Information Network.

20160603081241.6
rda

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