Gunther Schmidt, Thomas Ströhlein

Relations and Graphs

Discrete Mathematics for Computer Scientists

• Broschiertes Buch

Produktbeschreibung

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.

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Produktdetails

• Monographs in Theoretical Computer Science. An EATCS Series
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Softcover reprint of the original 1st ed. 1993
• Seitenzahl: 320
• Erscheinungstermin: 16. Januar 2012
• Englisch
• Abmessung: 235mm x 155mm x 18mm
• Gewicht: 487g
• ISBN-13: 9783642779701
• ISBN-10: 3642779700
• Artikelnr.: 36120611

Inhaltsangabe

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.