The Domain Theory in Computer Science

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.