Relations and Graphs: Discrete Mathematics for Computer Scientists

by Gunther Schmidt, Thomas Ströhlein

Overview

Relational methods can be found at various places in computer science, notably in data base theory, relational semantics of concurrency, relationaltype theory, analysis of rewriting systems, and modern programming language design. In addition, they appear in algorithms analysis and in the bulk of discrete mathematics taught to computer scientists. This book is devoted to the background of these methods. It explains how to use relational and graph-theoretic methods systematically in computer science. A powerful formal framework of relational algebra is developed with respect to applications to a diverse range of problem areas. Results are first motivated by practical examples, often visualized by both Boolean 0-1-matrices and graphs, and then derived algebraically.

Product Details

ISBN-13:	9783642779701
Publisher:	Springer Berlin Heidelberg
Publication date:	01/16/2012
Series:	Monographs in Theoretical Computer Science. An EATCS Series
Edition description:	Softcover reprint of the original 1st ed. 1993
Pages:	301
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

1. Sets.- 2. Homogeneous Relations.- 2.1 Boolean Operations on Relations.- 2.2 Transposition of a Relation.- 2.3 The Product of Two Relations.- 2.4 Subsets and Points.- 2.5 References.- 3. Transitivity.- 3.1 Orderings and Equivalence Relations.- 3.2 Closures and Closure Algorithms.- 3.3 Extrema, Bounds, and Suprema.- 3.4 References.- 4. Heterogeneous Relations.- 4.1 Bipartite Graphs.- 4.2 Functions and Mappings.- 4.3 n-ary Relations in Data Bases.- 4.4 Difunctionality.- 4.5 References.- 5. Graphs: Associated Relation, Incidence, Adjacency.- 5.1 Directed Graphs.- 5.2 Graphs via the Associated Relation.- 5.3 Hypergraphs.- 5.4 Graphs via the Adjacency Relation.- 5.5 Incidence and Adjacency.- 5.6 References.- 6. Reachability.- 6.1 Paths and Circuits.- 6.2 Chains and Cycles.- 6.3 Terminality and Foundedness.- 6.4 Confluence and Church-Rosser Theorems.- 6.5 Hasse Diagrams and Discreteness.- 6.6 References.- 7. The Category of Graphs.- 7.1 Homomorphisms of 1-Graphs.- 7.2 More Graph Homomorphisms.- 7.3 Covering of Graphs and Path Equivalence.- 7.4 Congruences.- 7.5 Direct Product and n-ary Relations.- 7.6 References.- 8. Kernels and Games.- 8.1 Absorptiveness and Stability.- 8.2 Kernels.- 8.3 Games.- 8.4 References.- 9. Matchings and Coverings.- 9.1 Independence.- 9.2 Coverings.- 9.3 Matching Theorems.- 9.4 Starlikeness.- 9.5 References.- 10. Programs: Correctness and Verification.- 10.1 Programs and Their Effect.- 10.2 Partial Correctness and Verification.- 10.3 Total Correctness and Termination.- 10.4 Weakest Preconditions.- 10.5 Coverings of Programs.- 10.6 References.- General References.- Name Index.- Table of Symbols.