An Introduction to Formal Languages and Automata (Solution)

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Description: Written to address the fundamentals of formal languages, automata, and computability, An Introduction to Formal Languages and Automata, Fifth Edition, provides an accessible, student-friendly presentation of all the material essential to an introductory Theory of Computation course. It 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. In the new Fifth Edition, Peter Linz continues to offer a straightforward, uncomplicated treatment of formal languages and automata and avoids excessive mathematical detail so that students may focus on and understand the underlying principles. The new edition also features a close connection between the text and JFLAP, which lets students follow difficult constructions and examples step-by-step, thus increasing understanding and insight.

New and Key Features of the revised and updated Fifth Edition:

• Includes a new chapter within the appendices on finite-state transducers, including basic results on Mealy and Moore machines. This optional chapter can be used to prepare students for further related study.

• Provides an introduction to JFLAP, also within the appendices. Many of the exercises in the text require creating structures that are complicated and must be tested for correctness. JFLAP can greatly reduce students’ time spent on testing as well as help them visualize abstract concepts.

Contents:
Preface • 1. Introduction to the Theory of Computation • Mathematical Preliminaries and Notation • Sets • Functions and Relations • Graphs and Trees • Proof Techniques • Three Basic Concepts • Languages • Grammars • Automata • Some Applications*

2. Finite Automata • Deterministic Finite Accepters • Deterministic Accepters and Transition Graphs • Languages and Dfa’s • Regular Languages • Nondeterministic Finite Accepters • Definition of a Nondeterministic Accepter • Why Nondeterminism? • Equivalence of Deterministic and Nondeterministic Finite Accepters • Reduction of the Number of States in Finite Automata*

3. Regular Languages and Regular Grammars • Regular Expressions • Formal Definition of a Regular Expression • Languages Associated with Regular Expressions • Connection Between Regular Expressions and Regular Languages • Regular Expressions Denote Regular Languages • Regular Expressions for Regular Languages • Regular Expressions for Describing Simple Patterns • 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 • Closure Properties of Regular Languages • Closure under Simple Set Operations • Closure under Other Operations • Elementary Questions about Regular Languages • Identifying Nonregular Languages • Using the Pigeonhole Principle • A Pumping Lemma

5. Context-Free Languages • Context-Free Grammars • Examples of Context-Free Languages • Leftmost and Rightmost Derivations • Derivation Trees • Relation Between Sentential Forms and Derivation Trees • Parsing and Ambiguity • Parsing and Membership • Ambiguity in Grammars and Languages • Context-Free Grammars and Programming Languages

6. Simplification of Context-Free Grammars and Normal Forms • Methods for Transforming Grammars • A Useful Substitution Rule • Removing Useless Productions • Removing ?-Productions • Removing Unit-Productions • Two Imprtant Normal Forms • Chomsky Normal Form • Greibach Normal Form • A Membership Algorithm for Context-Free Grammars*

7. Pushdown Automata • Nondeterministic Pushdown Automata • Definition of a Pushdown Automaton • The Language Accepted by a Pushdown Automaton • Pushdown Automata and Context-Free Languages • Pushdown Automata for Context-Free Languages • Context-Free Grammars for Pushdown Automata • Deterministic Pushdown Automata and Deterministic Context-Free Languages • Grammars for Deterministic Context-Free Languages*

8. Properties of Context-Free Languages • Two Pumping Lemmas • A Pumping Lemma for Context-Free Languages • A Pumping Lemma for Linear Languages • Closure Properties and Decision Algorithms for Context- Free Languages • Closure of Context-Free Languages • Some Decidable Properties of Context-Free Languages

9. Turing Machines • The Standard Turing Machine • Definition of a Turing Machine • Turing Machines as Language Accepters • Turing Machines as Transducers • Combining Turing Machines for Complicated Tasks • Turing’s Thesis

10. Other Models of Turing Machines • 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 • Turing Machines with More Complex Storage • Multitape Turing Machines • Multidimensional Turing Machines • Nondeterministic Turing Machines • A Universal Turing Machine • Linear Bounded Automata

11. A Hierarchy of Formal Languages and Automata • 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 • Unrestricted Grammars • Context-Sensitive Grammars and Languages • Context-Sensitive Languages and Linear Bounded • Automata • Relation Between Recursive and Context-Sensitive Languages • The Chomsky Hierarchy

12. Limits of Algorithmic Computation • Some Problems That Cannot Be Solved by Turing • Machines • Computability and Decidability • The Turing Machine Halting Problem • Reducing One Undecidable Problem to Another • Undecidable Problems for Recursively Enumerable • Languages • The Post Correspondence Problem • Undecidable Problems for Context-Free Languages • A Question of Efficiency

13. Other Models of Computation • Recursive Functions • Primitive Recursive Functions • Ackermann’s Function • µ Recursive Functions • Post Systems • Rewriting Systems • Matrix Grammars • Markov Algorithms • L-Systems

14. An Overview of Computational Complexity • Efficiency of Computation • Turing Machine Models and Complexity • Language Families and Complexity Classes • The Complexity Classes P and NP • Some NP Problems • Polynomial- Time Reduction • NP-Completeness and an Open Question • Appendix A Finite-State Transducers • Appendix B JFLAP: A Recommendation • Answers Solutions and Hints for Selected Exercises • References for Further Reading • Index.

About the Author: Peter Linz is Professor Emeritus in the Department of Computer Science at the University of California, Davis. Linz received his Ph.D. from the University of Wisconsin. Professor Linz’s research emphasizes the development of a theory of numerical analysis that can be used in the construction of reliable numerical methods used in the design of problem-solving environments for scientific computing. Linz has released the fourth edition of An Introduction to Formal Languages and Automata, as well as Exploring Numerical Methods: An Introduction to Scientific Computing.

Target Audience: Written to address the fundamentals of formal languages, automata, and computability, An Introduction to Formal Languages and Automata provides an accessible, student-friendly presentation of all material essential to an introductory Theory of Computation course.

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