Express Learning: Automata Theory and Formal Languages

377 Pages·2.138 MB·

by  Kandar, Shyamalendu

Automata Theory and Formal
Languages
Express Learning Series
This page is intentionally left blank.
Automata Theory and Formal
Languages
Express Learning Series
Shyamalendu Kandar
Assistant Professor
Computer Science and Engineering
Haldia Institute of Technology, Haldia
and
Course Co-ordinator
HIT Center M.Tech- IT(CWE)
Jadavpur University
Copyright © 2012 Dorling Kindersley (India) Pvt. Ltd.
Licensees of Pearson Education in South Asia
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ISBN 9788131760772
eISBN 9789332510319
Head Office: A-8(A), Sector 62, Knowledge Boulevard, 7th Floor, NOIDA 201 309, India
Registered Office: 11 Local Shopping Centre, Panchsheel Park, New Delhi 110 017, India
Dedication
To my parents,
Arun Kumar Kandar and Hirabati Kandar,
who have shown me the light of the universe and light of knowledge
&
My GURU in the fi eld of technical education
Professor C. T. Bhunia
who is an inspiration in every step of my life
About the Author
Shyamalendu Kandar is Assistant Professor of Computer Science and Engineering at the Haldia Insti-
tute of Technology, Haldia, West Bengal. He has passed B.Tech. in Computer Science from Vidyasagar
University in 2004 and M.Tech. in Information Technology (Courseware Engineering) from Jadavpur
University in 2006. His research interest is mainly in multimedia communication, image processing,
and automata theory. He has published a number of research papers in international journals and pre-
sented papers in international conferences.
Contents
About the Author VI
Foreword XI
Preface XIII
Acknowledgements XV
1. Finite State Machine 1
1.1 Basics of Automata 1
1.2 Finite State Machine 2
1.3 State Equivalence and Minimization of Machine 18
1.4 Incompletely Specifi ed Machine and Minimal Machine 23
1.5 Merger Graph and Compatibility Graph 26
1.6 Finite Memory and Defi nite Memory Machine 38
1.7 Information Lossless Machine and Inverse Machine 52
1.8 Inverse Machine 60
What We Have Learned So Far 63
Solved Problems 64
Multiple Choice Questions 92
Exercises 93
Fill in the Blanks 98
2. Language and Grammar 100
2.1 Basic Terminology and Defi nitions 100
2.2 Grammar and Language 101
2.3 Chomsky Hierarchy 102
2.4 Examples 104
2.5 Context-sensitive Grammar 112
What We Have Learned So Far 113
Solved Problems 113
Multiple Choice Questions 114
Exercises 115
Fill in the Blanks 116
VIII Contents
3. Finite Automata 118
3.1 Basics About Finite Automata 118
3.2 Transitional System 121
3.3 Deterministic Finite Automata and Non-Deterministic
Finite Automata 123
3.4 NFA with Null Move 128
3.5 Dead State 133
3.6 Finite Automata with Output 134
3.7 Conversion of Moore To Mealy Machine by Tabular Format 138
3.8 Conversion of Mealy to Moore Machine by Tabular Format 140
3.9 Conversion of Moore to Mealy Machine by Transitional Format 144
3.10 Conversion of Mealy to Moore Machine by Transitional Format 147
3.11 Minimization of Finite Automata 151
3.12 Myhill-Nerode Theorem 155
What We Have Learned So Far 161
Solved Problems 162
Multiple Choice Questions 176
Exercises 177
Fill in the Blanks 180
4. Regular Expression 182
4.1 Basics of Regular Expression 182
4.2 Arden Theorem 186
4.3 Construction of Finite Automata Equivalent
to a Regular Expression 191
4.4 NFA With Є Move and Conversion to DFA
By Є – Closure Method 196
4.5 Equivalence of Two Finite Automata and Two
Regular Expressions 202
4.6 Construction of Regular Grammar from
a Regular Expression 205
4.7 Pumping Lemma and its Application 208
4.8 Closure Properties of Regular Set 214
What We Have Learned So Far 218
Solved Problems 218
Multiple Choice Questions 227
Exercises 228
Fill in the Blanks 230
Contents IX
5. Context Free Grammar 232
5.1 Context Free Grammar: Defi nition and Examples 232
5.2 Derivation and Parse Tree 235
5.3 Ambiguity 239
5.4 Left Recursion and Left Factoring 243
5.5 Simplifi cation of CFG 246
5.6 Normal Form 254
5.7 Constructing FA from Regular Grammar 262
5.8 Closure Properties of CFL 264
5.9 Pumping Lemma for CFL 265
5.10 Ogden’s Lemma for CFL 269
5.11 Decision Algorithms 269
What We Have Learned So Far 271
Solved Problems 272
Multiple Choice Questions 285
Exercises 286
Fill in the Blanks 288
6. Pushdown Automata 291
6.1 Basics of Pushdown Automata 291
6.2 Acceptance by a PDA 293
6.3 Examples 294
6.4 Deterministic PDA and Non-Deterministic PDA 308
6.5 Pushdown Automata from Context Free Grammar 311
6.6 Graphical Notation for PDA 316
What We Have Learned So Far 317
Solved Problems 318
Multiple Choice Questions 328
Exercises 329
Fill in the Blanks 330
7. Turing Machine 331
7.1 Basic of Turing Machine 331
7.2 Examples 333
7.3 Transitional Representation of Turing Machine 346
What We Have Learned So Far 347
Solved Problems 348
Multiple Choice Questions 352
Exercises 353
Fill in the Blanks 353
References 355
Index 357