Computability, Complexity, and Languages, Second Edition:Fundamentals of Theoretical Computer Science (Computer Science and Scientific Computing)

Computability, Complexity, and Languages, Second Edition:Fundamentals of Theoretical Computer Science (Computer Science and Scientific Computing)
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出版社: Morgan Kaufmann
1994-02
ISBN: 9780122063824
装帧: 精装
开本: 其他
页数: 609页
1人买过
  • Preface
    Acknowledgments
    Dependency Graph
    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 Cmnputability
    2 Programs and Computable Functions
    1. A Programming Language
    2. Some Examples of Programs
    3. Syntax
    - 4. Computable Functions
    5. More about Macros
    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 Gijdel Numbers
    4 A Universal Program
    1. Coding Programs by Numbers
    - -- 2. The Halting Problem
    3. Universality
    4. Recursively Enumerable Sets
    5. The Parameter Theorem
    6. Diagonalization and Reducibility
    -_’  7. Rice’ s Theorem
    *8. The Recursion Theorem
    *9. A Computable Function That Is Not Primitive Recursive
    5 Calculations on Strings
    1. Numerical Representation of Strings
    2. A Programming Language for String Computations
    3. The Languages Y and Yn
    4. Post-Turing Programs
    5. Simulation  of-F”, in 9
    6. Simulation of Yin Y
    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
    7 Processes and Grammars
    1. Semi-Thue Processes
    2. Simulation of Nondeterministic Turing Machines by
    Semi-Thue Processes
    3.
    4.
    5.
    6.
    *7.
    Unsolvable Word Problems
    Post’ s Correspondence Problem
    Grammars
    Some Unsolvable Problems Concerning Grammars
    Normal Processes
    8 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
    Part 2 Grammars and Automata
    9 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
    10 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
    11 Context-Sensitive Languages
    1. The Chomsky Hierarchy
    2. Linear Bounded Automata
    3. Closure Properties
    Part 3 Logic
    12 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
    13 Quantification Theory
    1. The Language of Predicate Logic
    2. Semantics
    3. Logical Consequence
    4. Herbrand’ s Theorem
    5. Unification
    6. Compactness and Countability
    *7. Godel’ s Incompleteness Theorem
    *8. Unsolvability of the Satisfiability Problem in Predicate Logic
    Part 4 Complexity
    14 Abstract Complexity
    1. The Blum Axioms
    2. The Gap Theorem
    3. Preliminary Form of the Speedup Theorem
    4. The Speedup Theorem Concluded
    15 Polynomial-Time Computability
    1. Rates of Growth
    2. P versus NP
    3. Cook’ s Theorem
    4. Other NP-Complete Problems
    Part 5 Semantics
    16 Approximation Orderings
    1. Programming Language Semantics
    2. Partial Orders
    3. Complete Partial Orders
    4. Continuous Functions
    5. Fixed Points
    17 Denotational Semantics of Recursion Equations
    1. Syntax
    2. Semantics of Terms
    3. Solutions to W-Programs
    4. Denotational Semantics of W-Programs
    5. Simple Data Structure Systems
    6. Infinitary Data Structure Systems
    18 Operational Semantics of Recursion Equations
    1. Operational Semantics for Simple Data Structure Systems
    2. Computable Functions
    3. Operational Semantics for Infinitary Data Structure Systems
  • 内容简介:
    Preface
    Acknowledgments
    Dependency Graph
    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 Cmnputability
    2 Programs and Computable Functions
    1. A Programming Language
    2. Some Examples of Programs
    3. Syntax
    - 4. Computable Functions
    5. More about Macros
    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 Gijdel Numbers
    4 A Universal Program
    1. Coding Programs by Numbers
    - -- 2. The Halting Problem
    3. Universality
    4. Recursively Enumerable Sets
    5. The Parameter Theorem
    6. Diagonalization and Reducibility
    -_’  7. Rice’ s Theorem
    *8. The Recursion Theorem
    *9. A Computable Function That Is Not Primitive Recursive
    5 Calculations on Strings
    1. Numerical Representation of Strings
    2. A Programming Language for String Computations
    3. The Languages Y and Yn
    4. Post-Turing Programs
    5. Simulation  of-F”, in 9
    6. Simulation of Yin Y
    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
    7 Processes and Grammars
    1. Semi-Thue Processes
    2. Simulation of Nondeterministic Turing Machines by
    Semi-Thue Processes
    3.
    4.
    5.
    6.
    *7.
    Unsolvable Word Problems
    Post’ s Correspondence Problem
    Grammars
    Some Unsolvable Problems Concerning Grammars
    Normal Processes
    8 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
    Part 2 Grammars and Automata
    9 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
    10 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
    11 Context-Sensitive Languages
    1. The Chomsky Hierarchy
    2. Linear Bounded Automata
    3. Closure Properties
    Part 3 Logic
    12 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
    13 Quantification Theory
    1. The Language of Predicate Logic
    2. Semantics
    3. Logical Consequence
    4. Herbrand’ s Theorem
    5. Unification
    6. Compactness and Countability
    *7. Godel’ s Incompleteness Theorem
    *8. Unsolvability of the Satisfiability Problem in Predicate Logic
    Part 4 Complexity
    14 Abstract Complexity
    1. The Blum Axioms
    2. The Gap Theorem
    3. Preliminary Form of the Speedup Theorem
    4. The Speedup Theorem Concluded
    15 Polynomial-Time Computability
    1. Rates of Growth
    2. P versus NP
    3. Cook’ s Theorem
    4. Other NP-Complete Problems
    Part 5 Semantics
    16 Approximation Orderings
    1. Programming Language Semantics
    2. Partial Orders
    3. Complete Partial Orders
    4. Continuous Functions
    5. Fixed Points
    17 Denotational Semantics of Recursion Equations
    1. Syntax
    2. Semantics of Terms
    3. Solutions to W-Programs
    4. Denotational Semantics of W-Programs
    5. Simple Data Structure Systems
    6. Infinitary Data Structure Systems
    18 Operational Semantics of Recursion Equations
    1. Operational Semantics for Simple Data Structure Systems
    2. Computable Functions
    3. Operational Semantics for Infinitary Data Structure Systems
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