Relational methods can be found at various places incomputer science, notably in data base theory, relationalsemantics of concurrency, relationaltype theory, analysisof rewriting systems, and modern programming languagedesign. In addition, they appear in algorithms analysis andin the bulk of discrete mathematics taught to computerscientists.This book is devoted to the background of these methods. Itexplains how to use relational and graph-theoretic methodssystematically in computer science.A powerful formal framework of relational algebra isdeveloped with respect to applications to a diverse range ofproblem areas. Results are first motivated by practicalexamples, often visualized by both Boolean 0-1-matrices andgraphs, and then derived algebraically.|Relational methods can be found at various places incomputer science, notably in data base theory, relationalsemantics of concurrency, relationaltype theory, analysisof rewriting systems, and modern programming languagedesign. In addition, they appear in algorithms analysis andin the bulk of discrete mathematics taught to computerscientists.This book is devoted to the background of these methods. Itexplains how to use relational and graph-theoretic methodssystematically in computer science.A powerful formal framework of relational algebra isdeveloped with respect to applications to a diverse range ofproblem areas. Results are first motivated by practicalexamples, often visualized by both Boolean 0-1-matrices andgraphs, and then derived algebraically.|This book explains how to use relational and graph-theoretic methods systematically in computer science. Results are first motivated by practical examples and then derived algebraically.
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.
Inhaltsverzeichnis
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.
Klappentext
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.
This book explains how to use relational and graph-theoretic methods systematically in computer science. Results are first motivated by practical examples and then derived algebraically.
