Computer Science Press An Introduction to the Theory of Computation 1st Edition by Eitan Gurari ISBN

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Author: Eitan Gurari

Computer Science Press An Introduction to the Theory of Computation 1st Table of contents:

Chapter 1: Introduction

• 1.1 What is Theoretical Computer Science?
• 1.2 The Role of Computation in Computer Science
• 1.3 The Relationship Between Theory and Practice
• 1.4 Overview of Computation Models

Chapter 2: Finite Automata

• 2.1 Deterministic Finite Automata (DFA)
• 2.2 Nondeterministic Finite Automata (NFA)
• 2.3 Equivalence of DFA and NFA
• 2.4 Regular Languages
• 2.5 Regular Expressions
• 2.6 Minimization of Finite Automata
• 2.7 Applications of Finite Automata

Chapter 3: Regular Languages

• 3.1 Closure Properties of Regular Languages
• 3.2 The Pumping Lemma for Regular Languages
• 3.3 Non-Regular Languages and the Pumping Lemma
• 3.4 Decision Algorithms for Regular Languages
• 3.5 Applications of Regular Languages

Chapter 4: Context-Free Grammars

• 4.1 Definition and Examples of Context-Free Grammars (CFG)
• 4.2 Derivations and Parse Trees
• 4.3 The Chomsky Normal Form
• 4.4 Context-Free Languages
• 4.5 Ambiguity in Context-Free Grammars
• 4.6 Applications of Context-Free Grammars

Chapter 5: Pushdown Automata

• 5.1 The Definition of a Pushdown Automaton (PDA)
• 5.2 Deterministic vs. Nondeterministic Pushdown Automata
• 5.3 Equivalence of PDAs and Context-Free Languages
• 5.4 The Pumping Lemma for Context-Free Languages
• 5.5 Applications of Pushdown Automata

Chapter 6: Turing Machines

• 6.1 The Turing Machine Model of Computation
• 6.2 Formal Definition of a Turing Machine
• 6.3 Variants of Turing Machines
• 6.4 The Church-Turing Thesis
• 6.5 Decidability and Recognizability
• 6.6 Halting Problem and Undecidability

Chapter 7: Computability

• 7.1 The Class of Computable Functions
• 7.2 The Halting Problem and Reductions
• 7.3 Rice’s Theorem
• 7.4 Unsolvable Problems in Computation
• 7.5 The Limits of Computation

Chapter 8: Complexity Theory

• 8.1 The P vs NP Problem
• 8.2 Complexity Classes: P, NP, and NP-Complete
• 8.3 The Cook-Levin Theorem and NP-Completeness
• 8.4 Reductions Between NP-Complete Problems
• 8.5 Approximation Algorithms for NP-Hard Problems
• 8.6 Space Complexity and PSPACE

Chapter 9: Time Complexity

• 9.1 Time Complexity Classes: O, Ω, and Θ Notations
• 9.2 Analyzing Algorithms and Time Complexity
• 9.3 The Class NP and Its Relationship to P
• 9.4 Polynomial-Time Reductions
• 9.5 The Hierarchy Theorem

Chapter 10: Advanced Topics in Computability and Complexity

• 10.1 Hierarchies of Complexity Classes
• 10.2 Interactive Proofs and Cryptographic Protocols
• 10.3 Quantum Computing and Computability
• 10.4 Complexity of Approximation and Parallel Computation
• 10.5 The Limits of Efficient Computation

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