Problems and exercises in discrete mathematics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Dordrecht [u.a.]
Kluwer
1996
|
| Series: | Kluwer texts in the mathematical sciences
14 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 422 S. |
| ISBN: | 0792340361 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface ix
I PROBLEMS 1
1 Representations of Boolean Functions 3
1.1 Tabular Representations 3
1.2 Formulas 8
1.3 Disjunctive and Conjunctive Normal Forms 20
1.4 Polynomials 25
1.5 Essential and Unessential Variables 30
2 Closed Classes and Completeness in Boolean Algebra 38
2.1 Closure Operation 38
2.2 Self Dual Functions 43
2.3 Linear Functions 47
2.4 Functions Preserving the Constants 52
2.5 Monotone Functions 55
2.6 Completeness and Closed Classes 60
3 Many Valued Logics 66
3.1 Formulas of A Valued Logics 66
3.2 Closed Classes and Completeness in ^ valued logic 71
4 Graphs and Networks 81
4.1 Basic Concepts of Graph Theory 81
4.2 Planarity, Connectivity, and Numerical Characteristics of Graphs . . 88
4.3 Directed Graphs 93
4.4 Trees and Bipolar Networks 98
5 Elements of Coding Theory 110
5.1 Hamming s Distance 110
5.2 Hamming s Codes 113
5.3 Linear Codes 118
5.4 Alphabetic Code Divisibility 122
5.5 Optimal Codes 127
6 Finite Automata 134
6.1 Determined and Boundedly Determined Functions 134
6.2 Diagrams, Equations, and Circuits 148
v
vi CONTENTS
6.3 Closed Classes and Completeness in Automata 182
7 Elements of Algorithm Theory 188
7.1 Turing Machines 188
7.2 Recursive Functions 202
7.3 Computability 209
8 Combinatorics 214
8.1 Permutations and Combinations 214
8.2 Inclusion and Exclusion Formula 224
8.3 Recurrences and Generating Functions 228
8.4 Polya s Theory 236
8.5 Asymptotics and Inequalities 240
8.6 Estimates in Graph Theory 248
9 Boolean Minimization 254
9.1 Faces of the n cube. Covers and tests for tables 254
9.2 Constructing of the Reduced Disjunctive Normal Form Methods . . . 260
9.3 Irredundant, Minimal, and Shortest DNFs 266
10 Logical Design 273
10.1 Circuits of Logical Elements 273
10.2 Contact Circuits 280
11 ANSWERS, HINTS, SOLUTIONS 295
1 Representations of Boolean Functions 297
1.1 Tabular Representations 297
1.2 Formulas 297
1.3 Disjunctive and Conjunctive Normal Forms 299
1.4 Polynomials 299
1.5 Essential and Unessential Variables 300
2 Closed Classes and Completeness in Boolean Algebra 303
2.1 Closure Operation 303
2.2 Self Dual Functions 305
2.3 Linear Functions 306
2.4 Functions Preserving the Constants 307
2.5 Monotone Functions 309
2.6 Completeness and Closed Classes 311
3 Many Valued Logics 313
3.1 Formulas of k Valued Logics 313
3.2 Closed Classes and Completeness in A Valued logic 315
CONTENTS vii
4 Graphs and Networks 325
4.1 Basic Concepts of Graph Theory 325
4.2 Planarity, Connectivity, and Numerical Characteristics of Graphs . . 326
4.3 Directed Graphs 327
4.4 Trees and Bipolar Networks 328
5 Elements of Coding Theory 329
5.1 Hamming s Distance 329
5.2 Hamming s Codes 331
5.3 Linear Codes 333
5.4 Alphabetic Code Divisibility 335
5.5 Optimal Codes 337
6 Finite Automata 339
6.1 Determined and Boundedly Determined Functions 339
6.2 Diagrams, Equations, and Circuits 341
6.3 Closed Classes and Completeness in Automata 345
7 Elements of Algorithm Theory 348
7.1 Turing Machines 348
7.2 Recursive Functions 349
7.3 Computability 351
8 Combinatorics 353
8.1 Permutations and Combinations 353
8.2 Inclusion and Exclusion Formula 363
8.3 Recurrences and Generating Functions 368
8.4 Polya s Theory 379
8.5 Asymptotics and Inequalities 383
8.6 Estimates in Graph Theory 401
9 Boolean Minimization 403
9.1 Faces of the rc cube. Covers and tests for tables 403
9.2 Constructing of the Reduced DNF Methods 406
9.3 Irredundant, Minimal, and Shortest DNFs 408
10 Logical Design 409
10.1 Circuits of Logical Elements 409
10.2 Contact Circuits 410
Bibliography 415
Index 419
|
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| isbn | 0792340361 |
| language | English Russian |
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| physical | XI, 422 S. |
| publishDate | 1996 |
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| publisher | Kluwer |
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| series | Kluwer texts in the mathematical sciences |
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| spelling | Gavrilov, Garij Petrovič 1935-1999 Verfasser (DE-588)172093252 aut Problems and exercises in discrete mathematics by G. P. Gavrilov and A. A. Sapozhenko Dordrecht [u.a.] Kluwer 1996 XI, 422 S. txt rdacontent n rdamedia nc rdacarrier Kluwer texts in the mathematical sciences 14 Mathématiques - Problèmes et exercices ram Informatik Mathematik Computer science Mathematics Problems, exercises, etc Mathematics Problems, exercises, etc Diskrete Mathematik (DE-588)4129143-8 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Diskrete Mathematik (DE-588)4129143-8 s DE-604 Sapoženko, A. A. Verfasser aut Kluwer texts in the mathematical sciences 14 (DE-604)BV005450041 14 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007400266&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gavrilov, Garij Petrovič 1935-1999 Sapoženko, A. A. Problems and exercises in discrete mathematics Kluwer texts in the mathematical sciences Mathématiques - Problèmes et exercices ram Informatik Mathematik Computer science Mathematics Problems, exercises, etc Mathematics Problems, exercises, etc Diskrete Mathematik (DE-588)4129143-8 gnd |
| subject_GND | (DE-588)4129143-8 (DE-588)4143389-0 |
| title | Problems and exercises in discrete mathematics |
| title_auth | Problems and exercises in discrete mathematics |
| title_exact_search | Problems and exercises in discrete mathematics |
| title_full | Problems and exercises in discrete mathematics by G. P. Gavrilov and A. A. Sapozhenko |
| title_fullStr | Problems and exercises in discrete mathematics by G. P. Gavrilov and A. A. Sapozhenko |
| title_full_unstemmed | Problems and exercises in discrete mathematics by G. P. Gavrilov and A. A. Sapozhenko |
| title_short | Problems and exercises in discrete mathematics |
| title_sort | problems and exercises in discrete mathematics |
| topic | Mathématiques - Problèmes et exercices ram Informatik Mathematik Computer science Mathematics Problems, exercises, etc Mathematics Problems, exercises, etc Diskrete Mathematik (DE-588)4129143-8 gnd |
| topic_facet | Mathématiques - Problèmes et exercices Informatik Mathematik Computer science Mathematics Problems, exercises, etc Mathematics Problems, exercises, etc Diskrete Mathematik Aufgabensammlung |
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