Relations and Graphs: Discrete Mathematics for Computer ScientistsSpringer Science & Business Media, 6 déc. 2012 - 301 pages 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. |
Table des matières
1 | |
Reachability | 18 |
3 | 28 |
3 | 101 |
2 | 115 |
4 | 127 |
Homomorphisms of 1Graphs | 142 |
5 | 153 |
6 | 171 |
4 | 196 |
4 | 221 |
5 | 228 |
Appendix | 265 |
Fixedpoint Theorems and Antimorphisms | 278 |
288 | |
295 | |
Autres éditions - Tout afficher
Relations and Graphs: Discrete Mathematics for Computer Scientists Gunther Schmidt,Thomas Ströhlein Aucun aperçu disponible - 1993 |
Relations and Graphs: Discrete Mathematics for Computer Scientists Gunther Schmidt,Thomas Ströhlein Aucun aperçu disponible - 2012 |
Expressions et termes fréquents
1-graph absorbant set adjacency arcs arrows associated relation bipartitioned graph Boolean lattice called circuits complement complete lattice condition confluence consider contains Corollary covering defined Definition directed graphs edge-adjacency edge-connecting element equivalence relation example exists finite graph fixedpoint flowgraph following holds functional given graph G Hasse diagram homogeneous relation homomorphism hyperedge hypergraph incidence inclusion infimum injective isomorphism isotonic iteration kernel Math matrix move obtain ordering pair path of infinite player point axiom point set position postcondition precisely predicate program steps progressively bounded progressively finite Proof Prop Proposition prove reachability relation algebra relation-algebraic respect rooted graph rooted tree satisfies Sect sequence simple graph strict-ordering strongly connected components subset successor surjective symmetric syq(A terminal points theorem total correctness transitive closure univalent univalent relations upper bound