Introduction to Theory of Automata, Formal Languages, and Computation
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2 Introduction to Theory of Automata, Formal Languages, and Computation
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4 Introduction to Theory of Automata, Formal Languages, and Computation Debidas Ghosh Professor and Founder-Head Department of Computer Science & Engineering Former Director-in-Charge National Institute of Technology Durgapur and Former Pro-Vice-Chancellor KIIT University, Bhubaneswar Delhi
5 Introduction to Theory of Automata, Formal Languages, and Computation Debidas Ghosh 2013 by PHI Learning Private Limited, Delhi. All rights reserved. No part of this book may be reproduced in any form, by mimeograph or any other means, without permission in writing from the publisher. ISBN The export rights of this book are vested solely with the publisher. Published by Asoke K. Ghosh, PHI Learning Private Limited, Rimjhim House, 111, Patparganj Industrial Estate, Delhi and Printed by Raj Press, New Delhi
6 To the Memory of My Parents
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8 Contents Preface xiii Acknowledgements Notation xix xvii 1. Preliminary Mathematical Review Sets and Subsets Venn Diagram Properties of Set Operations Two Special Properties of Set Operations Relations and Functions Relations Function Types of Function Notation of Permutation Graphs Some Terminologies Trees Proof Techniques Proof by Induction Proof by Contradiction 19 Exercises Three Basic Concepts: Grammar, Languages and Automata Strings and Languages Some Basic Terminologies Some Properties of String Concatenation Some Basic Language Operations Grammars Equivalent Grammars Chomsky Hierarchy of Grammars Automata 31 Exercises 32 vii
9 viii Contents 3. Finite Automata Description of Finite Automata Deterministic Finite Automata and Transition Graph Languages and DFA Regular Languages Non-deterministic Finite Automata Languages and NFA Equivalence of Deterministic and Non-deterministic Finite Automata Conversion from NFA to DFA Non-deterministic Finite Automaton with l-transitions Finite Automata with Binary Output Mealy Machine Moore Machine Transformation of Mealy to Moore Machines Transformation from Moore Machine to Mealy Machine Reduction of Number of States in Finite Automata 51 Exercises Regular Languages and Regular Grammars Regular Expressions Formal Definition of a Regular Expression Regular Languages (RLs) Regular Sets Equivalence of Two Regular Expressions Connection between REs and RLs Finite Automata and Regular Expression Regular Grammars Right-Linear Grammar Left-Linear Grammar Equivalence between Regular Languages and Regular Grammars 72 Exercises Properties of Regular Languages Closure Properties of Regular Languages Closure with Respect to Set Operations Closure with Respect to Other Operations Identifying Non-regular Languages The Pigeonhole Principle Pumping Lemma for Regular Languages 81 Exercises Context-Free Languages Context-Free Grammars Leftmost and Rightmost Derivations Derivation Trees 89
10 Contents ix Partial Derivation Trees Relation between Sentential Form and Derivation Tree Parsing and Ambiguity Parsing Ambiguity Inherently Ambiguous Context-Free Grammar and Programming Language Simple Grammar Simplification of Context-Free Grammars Substitution Rule Useless Production Removal l-production Removal Unit Production Removal Normal Forms Chomsky Normal Form (CNF) Greibach Normal Form (GNF) 105 Exercises Pushdown Automata Non-deterministic Pushdown Automata Configuration NPDA and Context-Free Languages Context-free Grammars for Pushdown Automata Deterministic Pushdown Automata Deterministic Context-Free Languages Grammars for Deterministic Context-Free Languages 126 Exercises Properties of Context-Free Languages Pumping Lemma for Context-Free Languages Pumping Lemma for Linear Language Closure Properties of Context-Free Languages 133 Exercises Turing Machine Standard Turing Machine Model Representation of Turing Machine Instantaneous Move Description Representation by Transition Table Representation by Transition Diagram Turing Machine as Language Accepter Turing Machine as Transducers Church Turing Thesis Design of a Turing Machine 147 Exercises 150
11 Introduction To Theory Of Automata,Formal Languages And Computation 30% OFF Publisher : PHI Learning ISBN : Author : Debidas Ghosh Type the URL : Get this ebook
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