Discrete computational structures
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| Main Author | |
|---|---|
| Format | eBook Book |
| Language | English |
| Published |
New York
Academic Press
1974
Elsevier Science & Technology |
| Edition | 1 |
| Subjects | |
| Online Access | Get full text |
| ISBN | 0124208509 9780124208506 |
Cover
Table of Contents:
- 1. DEFINITIONS OF GROUPS AND SUBGROUPS -- 2. GROUPS OF GRAPHS -- 3. GRAPHS OF GROUPS -- 4. GENERATORS AND RELATIONS -- 5. PERMUTATIONS AND PERMUTATION GROUPS -- 6. PERMUTATION GENERATORS -- Chapter 7. Partial Orders and Lattices -- 1. INTRODUCTION -- 2. PARTIAL ORDERS -- 3. LATTICES -- 4. SPECIALIZED LATTICES -- 5. ATOMIC LATTICES -- REFERENCE -- Chapter 8. Boolean Algebras -- 1. INTRODUCTION -- 2. PROPERTIES OF BOOLEAN ALGEBRAS -- 3. BOOLEAN ALGEBRAS AND SET ALGEBRAS -- 4. BOOLEAN FUNCTIONS -- 5. SWITCHING CIRCUITS -- 6. BOOLEAN FUNCTION MINIMIZATION -- 7. COMPUTER ARITHMETIC -- REFERENCE -- Chapter 9. The Propositional Calculus -- 1. INTRODUCTION -- 2. FUNDAMENTAL DEFINITIONS -- 3. TRUTH TABLES -- 4. WELL-FORMED FORMULAS -- 5. MINIMAL SETS OF OPERATORS -- 6. POLISH NOTATION -- 7. PROOFS IN LOGIC -- 8. SETS AND WORDSETS -- REFERENCE -- Chapter 10. Combinatorics -- 1. INTRODUCTION -- 2. PERMUTATIONS OF OBJECTS -- 3. COMBINATIONS OF OBJECTS -- 4. ENUMERATORS FOR COMBINATIONS -- 5. ENUMERATORS FOR PERMUTATIONS -- 6. STIRLING NUMBERS -- 7. CYCLE CLASSES OF PERMUTATIONS -- 8. PARTITIONS AND COMPOSITIONS -- REFERENCES -- Chapter 11. Systems of Distinct Representatives -- 1. INTRODUCTION AND HISTORY -- 2. THE THIRD QUESTION, GENERAL CASE -- 3. THE THIRD QUESTION, PARTITION CASE -- 4. SUMMARY -- REFERENCES -- Chapter 12. Discrete Probability -- 1. PROBABILITIES ON A DISCRETE SET -- 2. CONDITIONAL PROBABILITY AND INDEPENDENCE -- 3. COMPUTATION OF BINOMIAL COEFFICIENTS -- 4. DISTRIBUTIONS -- 5. RANDOM NUMBERS -- REFERENCE -- Answers and Hints for Selected Exercises -- Index -- Computer Science and Applied Mathematics
- Front Cover -- Discrete Computational Structures -- Copyright Page -- Table of Contents -- Preface -- Acknowledgments -- Chapter 1. Basic Forms and Operations -- 1. INTRODUCTION -- 2. ELEMENTS AND SETS -- 3. SUBSETS -- 4. VENN DIAGRAMS AND SET COMPLEMENTS -- 5. COMPUTER REPRESENTATION OF SETS -- 6. SET OPERATIONS -- 7. SET ALGEBRA -- 8. COMPUTER OPERATIONS ON SETS -- 9. PRODUCT SETS -- 10. RELATIONS, MAPPINGS, FUNCTIONS -- 11. EQUIVALENCE AND ORDER RELATIONS -- 11. EQUIVALENCE AND ORDER RELATIONS -- 12. THE LATTICE OF SUBSETS -- 13. VECTORS AND MATRICES -- Chapter 2. Undirected Graphs -- 1. GRAPH THEORY -- 2. BASIC DEFINITIONS -- 3. SPECIAL CLASSES OF GRAPHS -- 4. MATRIX REPRESENTATION OF GRAPHS -- 5. RELATIONS AMONG GRAPH MATRICES -- 6. INVARIANTS AND GRAPH ISOMORPHISM -- 7. CYCLE BASIS -- 8. MAXIMAL COMPLETE SUBGRAPHS -- 9. STORAGE MINIMIZATION FOR MATRICES -- 10. BANDWIDTH OF CUBIC GRAPHS -- 11. BANDWIDTH OF BIPARTITE GRAPHS -- 12. PLANAR GRAPHS AND THE FOUR COLOR CONJECTURE -- REFERENCES -- Chapter 3. Gorn Trees -- 1. INTRODUCTION -- 2. TREE DOMAINS -- 3. TREES -- 4. PREFIX REPRESENTATION AND TREE FORMS -- 5. EXPLICIT DEFINITIONS -- 6. SEARCHING, SUBROUTINES, AND THEOREM PROVING -- REFERENCES -- Chapter 4. Directed Graphs -- 1. INTRODUCTION -- 2. BASIC DEFINITIONS -- 3. SPECIAL CLASSES OF GRAPHS -- 4. MATRIX REPRESENTATION OF DIRECTED GRAPHS -- 5. FLOWCHARTS -- 6. NETWORKS -- 7. MINIMAL COST FLOWS -- 8. PRUNING BRANCHES TO FIND THE SHORTEST PATH -- 9. CRITICAL PATHS -- 10. GRAPHS OF MULTIPROCESSING SYSTEMS -- 11. INFORMATION NETWORKS -- REFERENCE -- Chapter 5. Formal and Natural Languages -- 1. INTRODUCTION -- 2. SEMIGROUPS -- 3. FORMAL LANGUAGES -- 4. BACKUS NAUR FORM AND ALGOL-LIKE LANGUAGES -- 5. SEMANTICS OF FORMAL LANGUAGES -- 6. NATURAL LANGUAGES -- REFERENCES -- Chapter 6. Finite Groups and Computing