P, NP, and NP-completeness: the basics of computational complexity
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2010
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| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Cover Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XXIX, 184 S. Ill. |
| ISBN: | 9780521192484 9780521122542 |
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MARC
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Record in the Search Index
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| adam_text | Contents page xi xiii xvii xxi xxv xxvii List of Figures Preface Overview To the Teacher Notations and Conventions Main Definitions and Results 1 1.1 1.2 1.3 Computational Tasks and Models Teaching Notes Representation Computational Tasks 1.2.1 Search Problems 1.2.2 Decision Problems 1.2.3 Promise Problems (an Advanced Comment) Uniform Models (Algorithms) 1.3.1 Overview and General Principles 1.3.2 A Concrete Model: Turing Machines 1.3.2.1 The Actual Model 1.3.2.2 The Church-Turing Thesis 1.3.3 Uncomputable Functions 1.3.3.1 On the Existence of Uncomputable Functions 1.3.3.2 The Halting Problem 1.3.3.3 A Few More Undecidability Results 1.3.4 Universal Algorithms 1.3.4.1 The Existence of Universal Algorithms 1.3.4.2 A Detour: Kolmogorov Complexity 1.3.5 Time (and Space) Complexity vii 1 2 3 5 5 6 8 8 9 11 12 16 18 18 19 21 22 23 24 26
viii Contents 1.3.6 Oracle Machines and Turing-Reductions 1.3.7 Restricted Models 1.4 Non-Uniform Models (Circuits and Advice) 1.4.1 Boolean Circuits 1.4.1.1 The Basic Model 1.4.1.2 Circuit Complexity 1.4.2 Machines That Take Advice 1.4.3 Restricted Models 1.4.3.1 Boolean Formulae 1.4.3.2 Other Restricted Classes of Circuits 1.5 Complexity Classes Exercises 29 31 31 32 32 35 36 37 38 39 40 41 2 48 49 50 53 54 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 3 The P versus NP Question Teaching Notes Efficient Computation The Search Version: Finding versus Checking 2.2.1 The Class P as a Natural Class of Search Problems 2.2.2 The Class NP as Another Natural Class of Search Problems 56 2.2.3 The P versus NP Question in Terms of Search Problems The Decision Version: Proving versus Verifying 2.3.1 The Class P as a Natural Class of Decision Problems 2.3.2 The Class NP and NP-Proof Systems 2.3.3 The P versus NP Question in Terms of Decision Problems Equivalence of the Two Formulations Technical Comments Regarding NP The Traditional Definition of NP In Support of P Being Different from NP Philosophical Meditations Exercises Polynomial-time Reductions Teaching Notes 3.1 The General Notion of a Reduction 3.1.1 The Actual Formulation 3.1.2 Special Cases 3.1.3 Terminology and a Brief Discussion 3.2 Reducing Optimization Problems to Search Problems 57 58 59 59 62 63 65 66 69 70 71 74 75 75 76 77 79 81
г Contents 3.3 Self-Reducibility of Search Problems 3.3.1 Examples 3.3.2 Self-Reducibility of NP-Complete Problems 3.4 Digest and General Perspective Exercises 4 ix 83 85 87 88 89 NP-Completeness Teaching Notes Definitions The Existence of NP-Complete Problems Bounded Halting and Non-Halting Some Natural NP-Complete Problems 4.3.1 Circuit and Formula Satisfiability: CSAT and SAT 4.3.1.1 The NP-Completeness of CSAT 4.3.1.2 The NP-Completeness of SAT 4.3.2 Combinatorics and Graph Theory 4.3.3 Additional Properties of the Standard Reductions 4.3.4 On the Negative Application of NP-Completeness 4.3.5 Positive Applications of NP-Completeness NP Sets That Are Neither in P nor NP-Complete Reflections on Complete Problems Exercises 96 97 98 99 102 103 104 105 109 113 120 121 122 126 130 133 Three Relatively Advanced Topics Teaching Notes 5.1 Promise Problems 5.1.1 Definitions 5.1.1.1 Search Problems with a Promise 5.1.1.2 Decision Problems with a Promise 5.1.1.3 Reducibility Among Promise Problems 5.1.2 Applications and Limitations 5.1.2.1 Formulating Natural Computational Problems 5.1.2.2 Restricting a Computational Problem 5.1.2.3 Non-generic Applications 5.1.2.4 Limitations 5.1.3 The Standard Convention of Avoiding Promise Problems 5.2 Optimal Search Algorithms for NP 5.3 The Class coNP and Its Intersection with NP Exercises 142 142 142 143 143 144 145 146 146 147 147 148 149 151 154 158 4.1 4.2 4.3 4.4 4.5 5
X Contents Historical Notes 165 Epilogue: A Brief Overview of Complexity Theory 169 Appendix: Some Computational Problems A.l Graphs A.2 Boolean Formulae 177 177 179 Bibliography Index 181 183
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| indexdate | 2024-07-09T22:44:10Z |
| institution | BVB |
| isbn | 9780521192484 9780521122542 |
| language | English |
| lccn | 2010023587 |
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| physical | XXIX, 184 S. Ill. |
| publishDate | 2010 |
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| publisher | Cambridge Univ. Press |
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| spelling | Goldreich, Oded 1957- Verfasser (DE-588)120549255 aut P, NP, and NP-completeness the basics of computational complexity Oded Goldreich 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2010 XXIX, 184 S. Ill. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Computational complexity Computer algorithms Approximation theory Polynomials Komplexitätstheorie (DE-588)4120591-1 gnd rswk-swf NP-vollständiges Problem (DE-588)4138229-8 gnd rswk-swf Berechnungstheorie (DE-588)4005581-4 gnd rswk-swf NP-vollständiges Problem (DE-588)4138229-8 s Berechnungstheorie (DE-588)4005581-4 s Komplexitätstheorie (DE-588)4120591-1 s DE-604 http://assets.cambridge.org/97805211/92484/cover/9780521192484.jpg Cover Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020532620&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Goldreich, Oded 1957- P, NP, and NP-completeness the basics of computational complexity Computational complexity Computer algorithms Approximation theory Polynomials Komplexitätstheorie (DE-588)4120591-1 gnd NP-vollständiges Problem (DE-588)4138229-8 gnd Berechnungstheorie (DE-588)4005581-4 gnd |
| subject_GND | (DE-588)4120591-1 (DE-588)4138229-8 (DE-588)4005581-4 |
| title | P, NP, and NP-completeness the basics of computational complexity |
| title_auth | P, NP, and NP-completeness the basics of computational complexity |
| title_exact_search | P, NP, and NP-completeness the basics of computational complexity |
| title_full | P, NP, and NP-completeness the basics of computational complexity Oded Goldreich |
| title_fullStr | P, NP, and NP-completeness the basics of computational complexity Oded Goldreich |
| title_full_unstemmed | P, NP, and NP-completeness the basics of computational complexity Oded Goldreich |
| title_short | P, NP, and NP-completeness |
| title_sort | p np and np completeness the basics of computational complexity |
| title_sub | the basics of computational complexity |
| topic | Computational complexity Computer algorithms Approximation theory Polynomials Komplexitätstheorie (DE-588)4120591-1 gnd NP-vollständiges Problem (DE-588)4138229-8 gnd Berechnungstheorie (DE-588)4005581-4 gnd |
| topic_facet | Computational complexity Computer algorithms Approximation theory Polynomials Komplexitätstheorie NP-vollständiges Problem Berechnungstheorie |
| url | http://assets.cambridge.org/97805211/92484/cover/9780521192484.jpg http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020532620&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT goldreichoded pnpandnpcompletenessthebasicsofcomputationalcomplexity |