Bibliographic record and links to related information available from the Library of Congress catalog.
Note: Contents data are machine generated based on pre-publication provided by the publisher. Contents may have variations from the printed book or be incomplete or contain other coding.
Table of Contents Automata The Methods and the Madness Why Study Automata Theory Introduction to Finite Automata Structural Representations Automata and Complexity Introduction to Formal Proof Deductive Proofs Reduction to De nitions Other Theorem Forms Theorems That Appear Not to Be If Then Statements Additional Forms of Proof Proving Equivalences About Sets The Contrapositive Proof by Contradiction Counterexamples Inductive Proofs Inductions on Integers More General Forms of Integer Inductions Structural Inductions Mutual Inductions The Central Concepts of Automata Theory Alphabets Strings Languages Problems Summary of Chapter Gradiance Problems for Chapter References for Chapter Finite Automata An Informal Picture of Finite Automata The Ground Rules The Protocol vii viii TABLE OF CONTENTS Enabling the Automata to Ignore Actions The Entire System as an Automaton Using the Product Automaton to Validate the Protocol Deterministic Finite Automata De nition of a Deterministic Finite Automaton How a DFA Processes Strings Simpler Notations for DFA s Extending the Transition Function to Strings The Language of a DFA Exercises for Section Nondeterministic Finite Automata An Informal View of Nondeterministic Finite Automata De nition of Nondeterministic Finite Automata The Extended Transition Function The Language of an NFA Equivalence of Deterministic and Nondeterministic Finite Automata A Bad Case for the Subset Construction Exercises for Section An Application Text Search Finding Strings in Text Nondeterministic Finite Automata for Text Search A DFA to Recognize a Set of Keywords Exercises for Section Finite Automata With Epsilon Transitions Uses of Transitions The Formal Notation for an NFA Epsilon Closures Extended Transitions and Languages for NFA s Eliminating Transitions Exercises for Section Summary of Chapter Gradiance Problems for Chapter References for Chapter Regular Expressions and Languages Regular Expressions The Operators of Regular Expressions Building Regular Expressions Precedence of Regular Expression Operators Exercises for Section Finite Automata and Regular Expressions From DFA s to Regular Expressions Converting DFA s to Regular Expressions by Eliminating States TABLE OF CONTENTS ix Converting Regular Expressions to Automata Exercises for Section Applications of Regular Expressions Regular Expressions in UNIX Lexical Analysis Finding Patterns in Text Exercises for Section Algebraic Laws for Regular Expressions Associativity and Commutativity Identities and Annihilators Distributive Laws The Idempotent Law Laws Involving Closures Discovering Laws for Regular Expressions The Test for a Regular Expression Algebraic Law Exercises for Section Summary of Chapter Gradiance Problems for Chapter References for Chapter Properties of Regular Languages Proving Languages Not to Be Regular The Pumping Lemma for Regular Languages Applications of the Pumping Lemma Exercises for Section Closure Properties of Regular Languages Closure of Regular Languages Under Boolean Operations Reversal Homomorphisms Inverse Homomorphisms Exercises for Section Decision Properties of Regular Languages Converting Among Representations Testing Emptiness of Regular Languages Testing Membership in a Regular Language Exercises for Section Equivalence and Minimization of Automata Testing Equivalence of States Testing Equivalence of Regular Languages Minimization of DFA s Why the Minimized DFA Can t Be Beaten Exercises for Section Summary of Chapter Gradiance Problems for Chapter References for Chapter x TABLE OF CONTENTS Context Free Grammars and Languages Context Free Grammars An Informal Example De nition of Context Free Grammars Derivations Using a Grammar Leftmost and Rightmost Derivations The Language of a Grammar Sentential Forms Exercises for Section Parse Trees Constructing Parse Trees The Yield of a Parse Tree Inference Derivations and Parse Trees From Inferences to Trees From Trees to Derivations From Derivations to Recursive Inferences Exercises for Section Applications of Context Free Grammars Parsers The YACC Parser Generator Markup Languages XML and Document Type De nitions Exercises for Section Ambiguity in Grammars and Languages Ambiguous Grammars Removing Ambiguity From Grammars Leftmost Derivations as a Way to Express Ambiguity Inherent Ambiguity Exercises for Section Summary of Chapter Gradiance Problems for Chapter References for Chapter Pushdown Automata De nition of the Pushdown Automaton Informal Introduction The Formal De nition of Pushdown Automata A Graphical Notation for PDA s Instantaneous Descriptions of a PDA Exercises for Section The Languages of a PDA Acceptance by Final State Acceptance by Empty Stack From Empty Stack to Final State From Final State to Empty Stack TABLE OF CONTENTS xi Exercises for Section Equivalence of PDA s and CFG s From Grammars to Pushdown Automata From PDA s to Grammars Exercises for Section Deterministic Pushdown Automata De nition of a Deterministic PDA Regular Languages and Deterministic PDA s DPDA s and Context Free Languages DPDA s and Ambiguous Grammars Exercises for Section Summary of Chapter Gradiance Problems for Chapter References for Chapter Properties of Context Free Languages Normal Forms for Context Free Grammars Eliminating Useless Symbols Computing the Generating and Reachable Symbols Eliminating Productions Eliminating Unit Productions Chomsky Normal Form Exercises for Section The Pumping Lemma for Context Free Languages The Size of Parse Trees Statement of the Pumping Lemma Applications of the Pumping Lemma for CFL s Exercises for Section Closure Properties of Context Free Languages Substitutions Applications of the Substitution Theorem Reversal Intersection With a Regular Language Inverse Homomorphism Exercises for Section Decision Properties of CFL s Complexity of Converting Among CFG s and PDA s Running Time of Conversion to Chomsky Normal Form Testing Emptiness of CFL s Testing Membership in a CFL Preview of Undecidable CFL Problems Exercises for Section Summary of Chapter Gradiance Problems for Chapter References for Chapter xii TABLE OF CONTENTS Introduction to Turing Machines Problems That Computers Cannot Solve Programs that Print Hello World The Hypothetical Hello World Tester Reducing One Problem to Another Exercises for Section The Turing Machine The Quest to Decide All Mathematical Questions Notation for the Turing Machine Instantaneous Descriptions for Turing Machines Transition Diagrams for Turing Machines The Language of a Turing Machine Turing Machines and Halting Exercises for Section Programming Techniques for Turing Machines Storage in the State Multiple Tracks Subroutines Exercises for Section Extensions to the Basic Turing Machine Multitape Turing Machines Equivalence of One Tape and Multitape TM s Running Time and the Many Tapes to One Construction Nondeterministic Turing Machines Exercises for Section Restricted Turing Machines Turing Machines With Semi in nite Tapes Multistack Machines Counter Machines The Power of Counter Machines Exercises for Section Turing Machines and Computers Simulating a Turing Machine by Computer Simulating a Computer by a Turing Machine Comparing the Running Times of Computers and Turing Machines Summary of Chapter Gradiance Problems for Chapter References for Chapter Undecidability A Language That Is Not Recursively Enumerable Enumerating the Binary Strings Codes for Turing Machines The Diagonalization Language TABLE OF CONTENTS xiii Proof That Ld Is Not Recursively Enumerable Exercises for Section An Undecidable Problem That Is RE Recursive Languages Complements of Recursive and RE languages The Universal Language Undecidability of the Universal Language Exercises for Section Undecidable Problems About Turing Machines Reductions Turing Machines That Accept the Empty Language Rice s Theorem and Properties of the RE Languages Problems about Turing Machine Speci cations Exercises for Section Post s Correspondence Problem De nition of Post s Correspondence Problem The Modi ed PCP Completion of the Proof of PCP Undecidability Exercises for Section Other Undecidable Problems Problems About Programs Undecidability of Ambiguity for CFG s The Complement of a List Language Exercises for Section Summary of Chapter Gradiance Problems for Chapter References for Chapter Intractable Problems The Classes P and NP Problems Solvable in Polynomial Time An Example Kruskal s Algorithm Nondeterministic Polynomial Time An NP Example The Traveling Salesman Problem Polynomial Time Reductions NP Complete Problems Exercises for Section An NP Complete Problem The Satis ability Problem Representing SAT Instances NP Completeness of the SAT Problem Exercises for Section A Restricted Satis ability Problem Normal Forms for Boolean Expressions Converting Expressions to CNF xiv TABLE OF CONTENTS NP Completeness of CSAT NP Completeness of SAT Exercises for Section Additional NP Complete Problems Describing NP complete Problems The Problem of Independent Sets The Node Cover Problem The Directed Hamilton Circuit Problem Undirected Hamilton Circuits and the TSP Summary of NP Complete Problems Exercises for Section Summary of Chapter Gradiance Problems for Chapter References for Chapter Additional Classes of Problems Complements of Languages in NP The Class of Languages Co NP NP Complete Problems and Co NP Exercises for Section Problems Solvable in Polynomial Space Polynomial Space Turing Machines Relationship of PS and NPS to Previously De ned Classes Deterministic and Nondeterministic Polynomial Space A Problem That Is Complete for PS PS Completeness Quanti ed Boolean Formulas Evaluating Quanti ed Boolean Formulas PS Completeness of the QBF Problem Exercises for Section Language Classes Based on Randomization Quicksort an Example of a Randomized Algorithm A Turing Machine Model Using Randomization The Language of a Randomized Turing Machine The Class RP Recognizing Languages in RP The Class ZPP Relationship Between RP and ZPP Relationships to the Classes P and NP The Complexity of Primality Testing The Importance of Testing Primality Introduction to Modular Arithmetic The Complexity of Modular Arithmetic Computations Random Polynomial Primality Testing Nondeterministic Primality Tests TABLE OF CONTENTS xv Exercises for Section Summary of Chapter Gradiance Problems for Chapter References for Chapter Index
Library of Congress Subject Headings for this publication: