Computability, complexity, and languages : fundamentals of theoretical computer science
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| Hauptverfasser: | , |
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| Format: | E-Book Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Orlando, Fla
Academic Press
1983
Elsevier Science & Technology |
| Ausgabe: | 1 |
| Schlagworte: | |
| ISBN: | 9780122063800, 0122063805 |
| Online-Zugang: | Volltext |
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Inhaltsangabe:
- CHAPTER 16. Classifying Unsolvable Problems -- 1. Using Oracles -- 2. Relativization of Universality -- 3. Reducibility -- 4. Sets R.E. Relative to an Oracle -- 5. The Arithmetic Hierarchy -- 6. Post's Theorem -- 7. Classifying Some Unsolvable Problems -- 8. Rice's Theorem Revisited -- 9. Recursive Permutations -- CHAPTER 17. Degrees of Unsolvability and Post's Problem -- 1. Turing Degrees -- 2. The Kleene-Post Theorem -- 3. Creative Sets-Myhill's Theorem -- 4. Simple Sets-Dekker's Theorem -- 5. Sacks's Splitting Theorem -- 6. The Priority Method -- Suggestions for Further Reading -- Index -- Computer Science and Applied Mathematics: A SERIES OF MONOGRAPHS AND TEXTBOOKS
- Front Cover -- Computability, Complexity, and Languages: Fundamentals of Theoretical Computer Science -- Copyright Page -- Table of Contents -- Dedication -- Preface -- Acknowledgments -- Dependency Graph -- CHAPTER 1. Preliminaries -- 1. Sets and n-tuples -- 2. Functions -- 3. Alphabets and Strings -- 4. Predicates -- 5. Quantifiers -- 6. Proof by Contradiction -- 7. Mathematical Induction -- PART 1: COMPUTABILITY -- CHAPTER 2. Programs and Computable Functions -- 1. A Programming Language -- 2. Some Examples of Programs -- 3. Syntax -- 4. Computable Functions -- 5. More about Macros -- CHAPTER 3. Primitive Recursive Functions -- 1. Composition -- 2. Recursion -- 3. PRC Classes -- 4. Some Primitive Recursive Functions -- 5. Primitive Recursive Predicates -- 6. Iterated Operations and Bounded Quantifiers -- 7. Minimalization -- 8. Pairing Functions and Gödel Numbers -- CHAPTER 4. A Universal Program -- 1. Coding Programs by Numbers -- 2. The Halting Problem -- 3. Universality -- 4. Recursively Enumerable Sets -- 5. The Parameter Theorem -- 6. The Recursion Theorem -- 7. Rice's Theorem -- CHAPTER 5. Calculations on Strings -- 1. Numerical Representation of Strings -- 2. A Programming Language for String Computations -- 3. The Languages ¥ and £f n -- 4. Post-Turing Programs -- CHAPTER 6. Turing Machines -- 1. Internal States -- 2. A Universal Turing Machine -- 3. The Languages Accepted by Turing Machines -- 4. The Halting Problem for Turing Machines -- 5. Nondeterministic Turing Machines -- 6. Variations on the Turing Machine Theme -- CHAPTER 7. Processes and Grammars -- 1. Semi-Thue Processes -- 2. Simulation of Nondeterministic Turing Machines by Semi-Thue Processes -- 3. Unsolvable Word Problems -- 4. Post's Correspondence Problem -- 5. Grammars -- 6. Some Unsolvable Problems Concerning Grammars -- 7. Recursion and Minimalization
- 8. Normal Processes -- 9. A Non-R.E. Set -- PART 2: GRAMMARS AND AUTOMATA -- CHAPTER 8. Regular Languages -- 1. Finite Automata -- 2. Nondeterministic Finite Automata -- 3. Additional Examples -- 4. Closure Properties -- 5. Kleene's Theorem -- 6. The Pumping Lemma and Its Applications -- 7. The Myhill-Nerode Theorem -- CHAPTER 9. Context-Free Languages -- 1. Context-Free Grammars and Their Derivation Trees -- 2. Regular Grammars -- 3. Chomsky Normal Form -- 4. Bar-Hillel's Pumping Lemma -- 5. Closure Properties -- 6. Solvable and Unsolvable Problems -- 7. Bracket Languages -- 8. Pushdown Automata -- 9. Compilers and Formal Languages -- CHAPTER 10. Context-Sensitive Languages -- 1. The Chomsky Hierarchy -- 2. Linear Bounded Automata -- 3. Closure Properties -- PART 3: LOGIC -- CHAPTER 11. Propositional Calculus -- 1. Formulas and Assignments -- 2. Tautological Inference -- 3. Normal Forms -- 4. The Davis-Putnam Rules -- 5. Minimal Unsatisfiability and Subsumption -- 6. Resolution -- 7. The Compactness Theorem -- CHAPTER 12. Quantification Theory -- 1. The Language of Predicate Logic -- 2. Semantics -- 3. Logical Consequence -- 4. Herbrand's Theorem -- 5. Unification -- 6. Compactness and Countability -- 7. Gödel's Incompleteness Theorem -- 8. Unsolvability of the Satisfiability Problem in Predicate Logic -- PART 4: COMPLEXITY -- CHAPTER 13. Loop Programs -- 1. The Language L and Primitive Recursive Functions -- 2. Running Time -- 3. S£n as a Hierarchy -- 4. A Converse to the Bounding Theorem -- 5. Doing without Branch Instructions -- CHAPTER 14. Abstract Complexity -- 1. The Blum Axioms -- 2. The Gap Theorem -- 3. Preliminary Form of the Speedup Theorem -- 4. The Speedup Theorem Concluded -- CHAPTER 15. Polynomial-Time Computability -- 1. Rates of Growth -- 2. P versus NP -- 3. Cook's Theorem -- 4. Other NP-Complete Problems -- PART 5: UNSOLVABILITY