نظریه دامنه در علوم کامپیوتر

This book covers different topics from domain theory in computer science, including: partial orders and groups, power domains and metrics, recursive data types (binary trees) and algebraicity and Boolean algebras. Section 1 focuses on partial orders and groups, describing characterizations and properties of a new partial order, natural partial orders on transformation semigroups with fixed sets, cyclic soft groups and their applications on groups, and factorization of groups involving symmetric and alternating groups. Section 2 focuses on power domains and metrics, describing FS+ domains, topology of GB-metric spaces, incoherency problems in a combination of description logics and rules, and metrics for multiset-theoretic subgraphs. Section 3 focuses on recursive data types (binary trees), describing binary tree’s recursion traversal algorithm and its improvement, the design of the minimum spanning tree algorithms, generating tree-lists by fusing individual tree detection and nearest neighbor imputation using airborne LIDAR data, a recursive approach to the Kauffman bracket, and a novel multiway splits decision tree for multiple types of data. Section 4 focuses on algebraicity and Boolean algebras, describing the deformation theory of structure constants for associative algebras, the Boolean algebra and central Galois algebras, the addition of sets in Boolean space as well as algebra and geometry of sets in Boolean space, and a multipath detection using Boolean satisfiability techniques. Cover Title Page Copyright DECLARATION ABOUT THE EDITOR TABLE OF CONTENTS List of Contributors List of Abbreviations Preface Section 1: Partial Orders and Groups Chapter 1 Some Characterizations and Properties of a New Partial Order Abstract Introduction Main Result Acknowledgments References Chapter 2 Natural Partial Orders on Transformation Semigroups with Fixed Sets Abstract Introduction Preliminaries and Notations Natural Partial Order on Fix(X, Y) Minimal and Maximal Elements Acknowledgments References Chapter 3 Cyclic Soft Groups and Their Applications on Groups Abstract Introduction Preliminaries The Order of Soft Groups Cyclic Soft Groups Conclusion References Chapter 4 Factorization of Groups Involving Symmetric and Alternating Groups Abstract Introduction Preliminary Results Main Results Acknowledgements References Section 2: Power Domains and Metrics Concepts Chapter 5 On FS+-Domains Abstract Introduction FS+-Domains Acknowledgments References Chapter 6 The Topology of GB-Metric Spaces Abstract Introduction The GB-Metric Spaces References Chapter 7 Incoherency Problems in a Combination of Description Logics and Rules Abstract Introduction and Motivation Hybrid MKNF Knowledge Bases Paracoherent Semantics for Hybrid MKNF Knowledge Base Suspicious MKNF Models Related Works Conclusion References Chapter 8 Metrics for Multiset-Theoretic Subgraphs Abstract Introduction Multisets Metrics Computations and Implementations Real World Application Conclusion Acknowledgments References Section 3: Recursive Functions and Data Types (Binary Trees) Chapter 9 Binary Tree’s Recursion Traversal Algorithm and Its Improvement Abstract Introduction Why Use a Binary Tree Traversal and Its Practical Application Binary Tree’s Recursive Traversal Algorithm and Description Another Algorithm of Binary Tree Traversal Algorithm-Non-Recursive Calls Algorithm Improvement of Non-Recursive Algorithm Conclusion Acknowledgements References Chapter 10 Generating Tree-Lists by Fusing Individual Tree Detection and Nearest Neighbor Imputation Using Airborne LiDAR Data Abstract Introduction Methods Results Discussion Conclusion References Chapter 11 A Recursive Approach to the Kauffman Bracket Abstract Introduction Basic Notions References Chapter 12 A Novel Multiway Splits Decision Tree for Multiple Types of Data Abstract Introduction Preliminaries Our Proposed Algorithm Experiments Conclusion Acknowledgments References Section 4: Algebraicity and Boolean Algebras Chapter 13 On the Deformation Theory of Structure Constants for Associative Algebras Abstract Introduction Deformations of the Structure Constants Generated by DDA Quantum, Discrete, and Coisotropic Deformations Three-Dimensional Lie Algebras as DDA Deformations Generated by General DDAs Nilpotent DDA Solvable DDAs Acknowledgment References Chapter 14 The Boolean Algebra and Central Galois algebras Abstract Introduction Definitions and Notations The Monomials and Subgroups Central Galois Algebras Acknowledgement References Chapter 15 On Addition of Sets in Boolean Space Abstract Equation in Sets Multisets References Chapter 16 Algebra and Geometry of Sets in Boolean Space Abstract Distance between Subsets Bn Sum of Sets in Bn Equations in Sets References Chapter 17 Multipath Detection Using Boolean Satisfiability Techniques Abstract Introduction Signal Model Boolean Satisfiability SAT Model for PN Code Acquisition Simulation Results Conclusions References Index Back Cover