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9780763737986

An Introduction to Formal Language And Automata

by
  • ISBN13:

    9780763737986

  • ISBN10:

    0763737984

  • Edition: 4th
  • Format: Hardcover
  • Copyright: 2006-02-15
  • Publisher: Jones & Bartlett
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Summary

Fully revised, The new Fourth Edition of an Introduction to Formal Languages and Automata provides an accessible, student-friendly presentation of all material essential to an introductory Theory of Computation course. The text was 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 Fourth Edition, author Peter Linz has offered 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. In an effort to further the accessibility and comprehension of the text, The author has added new illustrative examples throughout. Click here to download the first print run errata. Click here to download the second print run errata.

Table of Contents

Introduction to the Theory of Computationp. 1
Mathematical Preliminaries and Notationp. 3
Setsp. 3
Functions and Relationsp. 6
Graphs and Treesp. 8
Proof Techniquesp. 10
Three Basic Conceptsp. 16
Languagesp. 16
Grammarsp. 20
Automatap. 26
Some Applicationsp. 30
Finite Automatap. 37
Deterministic Finite Acceptersp. 38
Deterministic Accepters and Transition Graphsp. 38
Languages and Dfa'sp. 40
Regular Languagesp. 44
Nondeterministic Finite Acceptersp. 49
Definition of a Nondeterministic Accepterp. 49
Why Nondeterminism?p. 53
Equivalence of Deterministic and Nondeterministic Finite Acceptersp. 56
Reduction of the Number of States in Finite Automatap. 63
Regular Languages and Regular Grammarsp. 71
Regular Expressionsp. 71
Formal Definition of a Regular Expressionp. 72
Languages Associated with Regular Expressionsp. 72
Connection Between Regular Expressions and Regular Languagesp. 77
Regular Expressions Denote Regular Languagesp. 78
Regular Expressions for Regular Languagesp. 80
Regular Expressions for Describing Simple Patternsp. 86
Regular Grammarsp. 89
Right- and Left-Linear Grammarsp. 89
Right-Linear Grammars Generate Regular Languagesp. 91
Right-Linear Grammars for Regular Languagesp. 93
Equivalence of Regular Languages and Regular Grammarsp. 95
Properties of Regular Languagesp. 99
Closure Properties of Regular Languagesp. 100
Closure under Simple Set Operationsp. 100
Closure under Other Operationsp. 102
Elementary Questions about Regular Languagesp. 111
Identifying Nonregular Languagesp. 114
Using the Pigeonhole Principlep. 114
A Pumping Lemmap. 115
Context-Free Languagesp. 125
Context-Free Grammarsp. 126
Examples of Context-Free Languagesp. 127
Leftmost and Rightmost Derivationsp. 129
Derivation Treesp. 130
Relation between Sentential Forms and Derivation Treesp. 132
Parsing and Ambiguityp. 136
Parsing and Membershipp. 136
Ambiguity in Grammars and Languagesp. 140
Context-Free Grammars and Programming Languagesp. 146
Simplification of Context-Free Grammars and Normal Formsp. 149
Methods for Transforming Grammarsp. 150
A Useful Substitution Rulep. 150
Removing Useless Productionsp. 152
Removing [lambda]-Productionsp. 156
Removing Unit-Productionsp. 158
Two Important Normal Formsp. 164
Chomsky Normal Formp. 164
Greibach Normal Formp. 167
A Membership Algorithm for Context-Free Grammarsp. 171
Pushdown Automatap. 175
Nondeterministic Pushdown Automatap. 176
Definition of a Pushdown Automatonp. 176
The Language Accepted by a Pushdown Automatonp. 180
Pushdown Automata and Context-Free Languagesp. 185
Pushdown Automata for Context-Free Languagesp. 185
Context-Free Grammars for Pushdown Automatap. 190
Deterministic Pushdown Automata and Deterministic Context-Free Languagesp. 196
Grammars for Deterministic Context-Free Languagesp. 201
Properties of Context-Free Languagesp. 205
Two Pumping Lemmasp. 205
A Pumping Lemma for Context-Free Languagesp. 206
A Pumping Lemma for Linear Languagesp. 210
Closure Properties and Decision Algorithms for Context-Free Languagesp. 213
Closure of Context-Free Languagesp. 214
Some Decidable Properties of Context-Free Languagesp. 218
Turing Machinesp. 221
The Standard Turing Machinep. 222
Definition of a Turing Machinep. 222
Turing Machines as Language Acceptersp. 229
Turing Machines as Transducersp. 232
Combining Turing Machines for Complicated Tasksp. 238
Turing's Thesisp. 243
Other Models of Turing Machinesp. 249
Minor Variations on the Turing Machine Themep. 250
Equivalence of Classes of Automatap. 250
Turing Machines with a Stay-Optionp. 251
Turing Machines with Semi-Infinite Tapep. 253
The Off-Line Turing Machinep. 255
Turing Machines with More Complex Storagep. 258
Multitape Turing Machinesp. 258
Multidimensional Turing Machinesp. 260
Nondeterministic Turing Machinesp. 262
A Universal Turing Machinep. 266
Linear Bounded Automatap. 271
A Hierarchy of Formal Languages and Automatap. 275
Recursive and Recursively Enumerable Languagesp. 276
Languages That Are Not Recursively Enumerablep. 278
A Language That Is Not Recursively Enumerablep. 279
A Language That Is Recursively Enumerable but Not Recursivep. 281
Unrestricted Grammarsp. 282
Context-Sensitive Grammars and Languagesp. 289
Context-Sensitive Languages and Linear Bounded Automatap. 290
Relation Between Recursive and Context-Sensitive Languagesp. 292
The Chomsky Hierarchyp. 294
Limits of Algorithmic Computationp. 297
Some Problems That Cannot Be Solved by Turing Machinesp. 298
Computability and Decidabilityp. 298
The Turing Machine Halting Problemp. 299
Reducing One Undecidable Problem to Anotherp. 302
Undecidable Problems for Recursively Enumerable Languagesp. 306
The Post Correspondence Problemp. 309
Undecidable Problems for Context-Free Languagesp. 316
A Question of Efficiencyp. 320
Other Models of Computationp. 323
Recursive Functionsp. 325
Primitive Recursive Functionsp. 326
Ackermann's Functionp. 329
[micro] Recursive Functionsp. 331
Post Systemsp. 333
Rewriting Systemsp. 337
Matrix Grammarsp. 338
Markov Algorithmsp. 338
L-Systemsp. 340
An Overview of Computational Complexityp. 343
Efficiency of Computationp. 344
Turing Machine Models and Complexityp. 346
Language Families and Complexity Classesp. 349
The Complexity Classes P and NPp. 353
Some NP Problemsp. 354
Polynomial-Time Reductionp. 358
NP-Completeness and an Open Questionp. 360
Answersp. 363
Referencesp. 409
Indexp. 411
Table of Contents provided by Ingram. All Rights Reserved.

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