Introduction to Automata Theory, Languages, and Computation.

Hopcroft, John E.

Introduction to Automata Theory, Languages, and Computation. - 3rd ed. - 1 online resource (505 pages)

Cover -- Half Title -- Title -- Preface -- Table of Contents -- Chapter 1_Automata: The Methods and the Madness -- 1.1 Why Study Automata Theory? -- 1.1.1 Introduction to Finite Automata -- 1.1.2 Structural Representations -- 1.1.3 Automata and Complexity -- 1.2 Introduction to Formal Proof -- 1.2.1 Deductive Proofs -- 1.2.2 Reduction to Definitions -- 1.2.3 Other Theorem Forms -- 1.2.4 Theorems That Appear Not to Be If-Then Statements -- 1.3 Additional Forms of Proof -- 1.3.1 Proving Equivalences About Sets -- 1.3.2 The Contrapositive -- 1.3.3 Proof by Contradiction -- 1.3.4 Counterexamples -- 1.4 Inductive Proofs -- 1.4.1 Inductions on Integers -- 1.4.2 More General Forms of Integer Inductions -- 1.4.3 Structural Inductions -- 1.4.4 Mutual Inductions -- 1.5 The Central Concepts of Automata Theory -- 1.5.1 Alphabets -- 1.5.2 Strings -- 1.5.3 Languages -- 1.5.4 Problems -- 1.6 Summary of Chapter 1 -- 1.7 References for Chapter 1 -- Chapter 2_Finite Automata -- 2.1 An Informal Picture of Finite Automata -- 2.1.1 The Ground Rules -- 2.1.2 The Protocol -- 2.1.3 Enabling the Automata to Ignore Actions -- 2.1.4 The Entire System as an Automaton -- 2.1.5 Using the Product Automaton to Validate the Protocol -- 2.2 Deterministic Finite Automata -- 2.2.1 Definition of a Deterministic Finite Automaton -- 2.2.2 How a DFA Processes Strings -- 2.2.3 Simpler Notations for DFA's -- 2.2.4 Extending the Transition Function to Strings -- 2.2.5 The Language of a DFA -- 2.2.6 Exercises for Section 2.2 -- 2.3 Nondeterministic Finite Automata -- 2.3.1 An Informal View of Nondeterministic Finite Automata -- 2.3.2 Definition of Nondeterministic Finite Automata -- 2.3.3 The Extended Transition Function -- 2.3.4 The Language of an NFA -- 2.3.5 Equivalence of Deterministic and Nondeterministic Finite Automata -- 2.3.6 A Bad Case for the Subset Construction. 2.3.7 Exercises for Section 2.3 -- 2.4 An Application: Text Search -- 2.4.1 Finding Strings in Text -- 2.4.2 Nondeterministic Finite Automata for Text Search -- 2.4.3 A DFA to Recognize a Set of Keywords -- 2.4.4 Exercises for Section 2.4 -- 2.5 Finite Automata With Epsilon-Transitions -- 2.5.1 Uses of -Transitions -- 2.5.2 The Formal Notation for an -NFA -- 2.5.3 Epsilon-Closures -- 2.5.4 Extended Transitions and Languages for -NFA's -- 2.5.5 Eliminating -Transitions -- 2.5.6 Exercises for Section 2.5 -- 2.6 Summary of Chapter 2 -- 2.7 References for Chapter 2 -- Chapter 3_Regular Expressions and Languages -- 3.1 Regular Expressions -- 3.1.1 The Operators of Regular Expressions -- 3.1.2 Building Regular Expressions -- 3.1.3 Precedence of Regular-Expression Operators -- 3.1.4 Exercises for Section 3.1 -- 3.2 Finite Automata and Regular Expressions -- 3.2.1 From DFA's to Regular Expressions -- 3.2.2 Converting DFA's to Regular Expressions by Eliminating States -- 3.2.3 Converting Regular Expressions to Automata -- 3.2.4 Exercises for Section 3.2 -- 3.3 Applications of Regular Expressions -- 3.3.1 Regular Expressions in UNIX -- 3.3.2 Lexical Analysis -- 3.3.3 Finding Patterns in Text -- 3.3.4 Exercises for Section 3.3 -- 3.4 Algebraic Laws for Regular Expressions -- 3.4.1 Associativity and Commutativity -- 3.4.2 Identities and Annihilators -- 3.4.3 Distributive Laws -- 3.4.4 The Idempotent Law -- 3.4.5 Laws Involving Closures -- 3.4.6 Discovering Laws for Regular Expressions -- 3.4.7 The Test for a Regular-Expression Algebraic Law -- 3.4.8 Exercises for Section 3.4 -- 3.5 Summary of Chapter 3 -- 3.6 References for Chapter 3 -- Chapter 4_Properties of Regular Languages -- 4.1 Proving Languages Not to Be Regular -- 4.1.1 The Pumping Lemma for Regular Languages -- 4.1.2 Applications of the Pumping Lemma -- 4.1.3 Exercises for Section 4.1. 4.2 Closure Properties of Regular Languages -- 4.2.1 Closure of Regular Languages Under Boolean Operations -- 4.2.2 Reversal -- 4.2.3 Homomorphisms -- 4.2.4 Inverse Homomorphisms -- 4.2.5 Exercises for Section 4.2 -- 4.3 Decision Properties of Regular Languages -- 4.3.1 Converting Among Representations -- 4.3.2 Testing Emptiness of Regular Languages -- 4.3.3 Testing Membership in a Regular Language -- 4.3.4 Exercises for Section 4.3 -- 4.4 Equivalence and Minimization of Automata -- 4.4.1 Testing Equivalence of States -- 4.4.2 Testing Equivalence of Regular Languages -- 4.4.3 Minimization of DFA's -- 4.4.4 Why the Minimized DFA Can't Be Beaten -- 4.4.5 Exercises for Section 4.4 -- 4.5 Summary of Chapter 4 -- 4.6 References for Chapter 4 -- Chapter 5_Context-Free Grammars and Languages -- 5.1 Context-Free Grammars -- 5.1.1 An Informal Example -- 5.1.2 Definition of Context-Free Grammars -- 5.1.3 Derivations Using a Grammar -- 5.1.4 Leftmost and Rightmost Derivations -- 5.1.5 The Language of a Grammar -- 5.1.6 Sentential Forms -- 5.1.7 Exercises for Section 5.1 -- 5.2 Parse Trees -- 5.2.1 Constructing Parse Trees -- 5.2.2 The Yield of a Parse Tree -- 5.2.3 Inference, Derivations, and Parse Trees -- 5.2.4 From Inferences to Trees -- 5.2.5 From Trees to Derivations -- 5.2.6 From Derivations to Recursive Inferences -- 5.2.7 Exercises for Section 5.2 -- 5.3 Applications of Context-Free Grammars -- 5.3.1 Parsers -- 5.3.2 The YACC Parser-Generator -- 5.3.3 Markup Languages -- 5.3.4 XML and Document-Type Definitions -- 5.3.5 Exercises for Section 5.3 -- 5.4 Ambiguity in Grammars and Languages -- 5.4.1 Ambiguous Grammars -- 5.4.2 Removing Ambiguity From Grammars -- 5.4.3 Leftmost Derivations as a Way to Express Ambiguity -- 5.4.4 Inherent Ambiguity -- 5.4.5 Exercises for Section 5.4 -- 5.5 Summary of Chapter 5 -- 5.6 References for Chapter 5. Chapter 6_Pushdown Automata -- 6.1 Definition of the Pushdown Automaton -- 6.1.1 Informal Introduction -- 6.1.2 The Formal Definition of Pushdown Automata -- 6.1.3 A Graphical Notation for PDA's -- 6.1.4 Instantaneous Descriptions of a PDA -- 6.1.5 Exercises for Section 6.1 -- 6.2 The Languages of a PDA -- 6.2.1 Acceptance by Final State -- 6.2.2 Acceptance by Empty Stack -- 6.2.3 From Empty Stack to Final State -- 6.2.4 From Final State to Empty Stack -- 6.2.5 Exercises for Section 6.2 -- 6.3 Equivalence of PDA's and CFG's -- 6.3.1 From Grammars to Pushdown Automata -- 6.3.2 From PDA's to Grammars -- 6.3.3 Exercises for Section 6.3 -- 6.4 Deterministic Pushdown Automata -- 6.4.1 Definition of a Deterministic PDA -- 6.4.2 Regular Languages and Deterministic PDA's -- 6.4.3 DPDA's and Context-Free Languages -- 6.4.4 DPDA's and Ambiguous Grammars -- 6.4.5 Exercises for Section 6.4 -- 6.5 Summary of Chapter 6 -- 6.6 References for Chapter 6 -- Chapter 7_Properties of Context-FreeLanguages -- 7.1 Normal Forms for Context-Free Grammars -- 7.1.1 Eliminating Useless Symbols -- 7.1.2 Computing the Generating and Reachable Symbols -- 7.1.3 Eliminating -Productions -- 7.1.4 Eliminating Unit Productions -- 7.1.5 Chomsky Normal Form -- 7.1.6 Exercises for Section 7.1 -- 7.2 The Pumping Lemma for Context-Free Languages -- 7.2.1 The Size of Parse Trees -- 7.2.2 Statement of the Pumping Lemma -- 7.2.3 Applications of the Pumping Lemma for CFL's -- 7.2.4 Exercises for Section 7.2 -- 7.3 Closure Properties of Context-Free Languages -- 7.3.1 Substitutions -- 7.3.2 Applications of the Substitution Theorem -- 7.3.3 Reversal -- 7.3.4 Intersection With a Regular Language -- 7.3.5 Inverse Homomorphism -- 7.3.6 Exercises for Section 7.3 -- 7.4 Decision Properties of CFL's -- 7.4.1 Complexity of Converting Among CFG's and PDA's. 7.4.2 Running Time of Conversion to Chomsky Normal Form -- 7.4.3 Testing Emptiness of CFL's -- 7.4.4 Testing Membership in a CFL -- 7.4.5 Preview of Undecidable CFL Problems -- 7.4.6 Exercises for Section 7.4 -- 7.5 Summary of Chapter 7 -- 7.6 References for Chapter 7 -- Chapter 8_Introduction to Turing Machines -- 8.1 Problems That Computers Cannot Solve -- 8.1.1 Programs that Print "Hello, World" -- 8.1.2 The Hypothetical "Hello, World" Tester -- 8.1.3 Reducing One Problem to Another -- 8.1.4 Exercises for Section 8.1 -- 8.2 The Turing Machine -- 8.2.1 The Quest to Decide All Mathematical Questions -- 8.2.2 Notation for the Turing Machine -- 8.2.3 Instantaneous Descriptions for Turing Machines -- 8.2.4 Transition Diagrams for Turing Machines -- 8.2.5 The Language of a Turing Machine -- 8.2.6 Turing Machines and Halting -- 8.2.7 Exercises for Section 8.2 -- 8.3 Programming Techniques for Turing Machines -- 8.3.1 Storage in the State -- 8.3.2 Multiple Tracks -- 8.3.3 Subroutines -- 8.3.4 Exercises for Section 8.3 -- 8.4 Extensions to the Basic Turing Machine -- 8.4.1 Multitape Turing Machines -- 8.4.2 Equivalence of One-Tape and Multitape TM's -- 8.4.3 Running Time and the Many-Tapes-to-One Construction -- 8.4.4 Nondeterministic Turing Machines -- 8.4.5 Exercises for Section 8.4 -- 8.5 Restricted Turing Machines -- 8.5.1 Turing Machines With Semi-infinite Tapes -- 8.5.2 Multistack Machines -- 8.5.3 Counter Machines -- 8.5.4 The Power of Counter Machines -- 8.5.5 Exercises for Section 8.5 -- 8.6 Turing Machines and Computers -- 8.6.1 Simulating a Turing Machine by Computer -- 8.6.2 Simulating a Computer by a Turing Machine -- 8.6.3 Comparing the Running Times of Computers and Turing Machines -- 8.7 Summary of Chapter 8 -- 8.8 References for Chapter 8 -- Chapter 9_Undecidability -- 9.1 A Language That Is Not Recursively Enumerable. 9.1.1 Enumerating the Binary Strings.

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