An Introduction to Formal Languages and Automata

Description

An Introduction to Formal Languages and Automata, Sixth Edition provides an accessible, student-friendly presentation of all material essential to an introductory Theory of Computation course. Written to address the fundamentals of formal languages, automata, and computability, the text is designed to familiarize students with the foundations and principles of computer science and to strengthen the students' ability to carry out formal and rigorous mathematical arguments. The author, Peter Linz, continues to offer a straightforward, uncomplicated treatment of formal languages and automata and avoids excessive mathematical detail allowing students to focus on and understand the key underlying principles. Title Copyright CONTENTS PREFACE 1 INTRODUCTION TO THE THEORY OF COMPUTATION 1.1 Mathematical Preliminaries and Notation Sets Functions and Relations Graphs and Trees Proof Techniques 1.2 Three Basic Concepts Languages Grammars Automata 1.3 Some Applications* 2 FINITE AUTOMATA 2.1 Deterministic Finite Accepters Languages and Dfa’s Regular Languages 2.2 Nondeterministic Finite Accepters Definition of a Nondeterministic Accepter Why Nondeterminism? 2.3 Equivalence of Deterministic and Nondeterministic Finite Accepters 2.4 Reduction of the Number of States in Finite Automata* 3 REGULAR LANGUAGES AND REGULAR GRAMMARS 3.1 Regular Expressions Formal Definition of a Regular Expression Languages Associated with Regular Expressions 3.2 Connection Between Regular Expressions and Regular Languages Regular Expressions Denote Regular Languages Regular Expressions for Regular Languages Regular Expressions for Describing Simple Patterns 3.3 Regular Grammars Right- and Left-Linear Grammars Right-Linear Grammars Generate Regular Languages Right-Linear Grammars for Regular Languages Equivalence of Regular Languages and Regular Grammars 4 PROPERTIES OF REGULAR LANGUAGES 4.1 Closure Properties of Regular Languages Closure under Simple Set Operations Closure under Other Operations 4.2 Elementary Questions about Regular Languages 4.3 Identifying Nonregular Languages Using the Pigeonhole Principle A Pumping Lemma 5 CONTEXT-FREE LANGUAGES 5.1 Context-Free Grammars Examples of Context-Free Languages Leftmost and Rightmost Derivations Derivation Trees Relation Between Sentential Forms and Derivation Trees 5.2 Parsing and Ambiguity Parsing and Membership Ambiguity in Grammars and Languages 5.3 Context-Free Grammars and Programming Languages 6 SIMPLIFICATION OF CONTEXT-FREE GRAMMARS AND NORMAL FORMS 6.1 Methods for Transforming Grammars A Useful Substitution Rule Removing Useless Productions Removing λ-Productions Removing Unit-Productions 6.2 Two Important Normal Forms Chomsky Normal Form Greibach Normal Form 6.3 A Membership Algorithm for Context-Free Grammars* 7 PUSHDOWN AUTOMATA 7.1 Nondeterministic Pushdown Automata Definition of a Pushdown Automaton The Language Accepted by a Pushdown Automaton 7.2 Pushdown Automata and Context-Free Languages Pushdown Automata for Context-Free Languages Context-Free Grammars for Pushdown Automata 7.3 Deterministic Pushdown Automata and Deterministic Context-Free Languages 7.4 Grammars for Deterministic Context-Free Languages* 8 PROPERTIES OF CONTEXT-FREE LANGUAGES 8.1 Two Pumping Lemmas A Pumping Lemma for Context-Free Languages A Pumping Lemma for Linear Languages 8.2 Closure Properties and Decision Algorithms for Context-Free Languages Closure of Context-Free Languages Some Decidable Properties of Context-Free Languages 9 TURING MACHINES 9.1 The Standard Turing Machine Definition of a Turing Machine Turing Machines as Language Accepters Turing Machines as Transducers 9.2 Combining Turing Machines for Complicated Tasks 9.3 Turing’s Thesis 10 OTHER MODELS OF TURING MACHINES 10.1 Minor Variations on the Turing Machine Theme Equivalence of Classes of Automata Turing Machines with a Stay-Option Turing Machines with Semi-Infinite Tape The Off-Line Turing Machine 10.2 Turing Machines with More Complex Storage Multitape Turing Machines Multidimensional Turing Machines 10.3 Nondeterministic Turing Machines 10.4 A Universal Turing Machine 10.5 Linear Bounded Automata 11 A HIERARCHY OF FORMAL LANGUAGES AND AUTOMATA 11.1 Recursive and Recursively Enumerable Languages Languages That Are Not Recursively Enumerable A Language That Is Not Recursively Enumerable A Language That Is Recursively Enumerable but Not Recursive 11.2 Unrestricted Grammars 11.3 Context-Sensitive Grammars and Languages Context-Sensitive Languages and Linear Bounded Automata Relation Between Recursive and Context-Sensitive Languages 11.4 The Chomsky Hierarchy 12 LIMITS OF ALGORITHMIC COMPUTATION 12.1 Some Problems That Cannot Be Solved by Turing Machines Computability and Decidability The Turing Machine Halting Problem Reducing One Undecidable Problem to Another 12.2 Undecidable Problems for Recursively Enumerable Languages 12.3 The Post Correspondence Problem 12.4 Undecidable Problems for Context-Free Languages 12.5 A Question of Efficiency 13 OTHER MODELS OF COMPUTATION 13.1 Recursive Functions Primitive Recursive Functions Ackermann’s Function μ Recursive Functions 13.2 Post Systems 13.3 Rewriting Systems Matrix Grammars Markov Algorithms L-Systems 14 AN OVERVIEW OF COMPUTATIONAL COMPLEXITY 14.1 Efficiency of Computation 14.2 Turing Machine Models and Complexity 14.3 Language Families and Complexity Classes 14.4 The Complexity Classes P and NP 14.5 Some NP Problems 14.6 Polynomial-Time Reduction 14.7 NP-Completeness and an Open Question APPENDIX A: FINITE-STATE TRANSDUCERS A.1 A General Framework A.2 Mealy Machines A.3 Moore Machines A.4 Moore and Mealy Machine Equivalence A.5 Mealy Machine Minimization A.6 Moore Machine Minimization A.7 Limitations of Finite-State Transducers APPENDIX B: JFLAP: A USEFUL TOOL ANSWERS SOLUTIONS AND HINTS FOR SELECTED EXERCISES REFERENCES FOR FURTHER READING INDEX A B C D E F G H I J L M N O P R S T U V W Y Z