SYLLABUS. Introduction to Finite Automata, Central Concepts of Automata Theory. CHAPTER - 3 : REGULAR EXPRESSIONS AND LANGUAGES

Transcription

1 Contents i SYLLABUS UNIT - I CHAPTER - 1 : AUT UTOMA OMATA Introduction to Finite Automata, Central Concepts of Automata Theory. CHAPTER - 2 : FINITE AUT UTOMA OMATA An Informal Picture of Finite Automata, Deterministic Finite Automata, Nondeterministic Finite Automata, An Application, Finite Automata with Epsilon Transitions. CHAPTER - 3 : REGULAR EXPRESSIONS AND LANGUAGES Regular Expressions, Finite Automata and Regular Expressions, Applications of Regular Expressions, Algebraic Laws for Regular Expressions. UNIT - II CHAPTER - 4 : PROPERTIES OF REGULAR LANGUAGES Proving Languages not to be Regular, Closure Properties of Regular Languages, Decision Properties of Regular Languages, Equivalence and Minimization of Automata. CHAPTER - 5 : CONTEXT FREE GRAMMARS AND LANGUAGES Context Free Grammars, Parses Trees, Applications, Ambiguity in Grammars and Languages. UNIT - III CHAPTER - 6 : PUSHDOWN AUT UTOMA OMATA Definition, Languages of PDA, Equivalence of PDA s and CFG s Deterministic Pushdown Automata. CHAPTER - 7 : PROPERTIES OF CONTEXT FREE LANGUAGES Normal Forms for Context Free Grammars, Pumping Lemma, Closure Properties, Decision Properties of CFL s.

2 ii Contents UNIT - IV CHAPTER - 8 : INTRODUCTION TO TURING MACHINES UNIT - V Problems that Computers Cannot Solve, The Turing Machines, Programming Techniques for Turing Machines, Extensions to the Turing for Machines, Restricted Turing Machines, Turing Machines and Computers. CHAPTER - 9 : UNDECIDABILITY A Language That is Not Recursively Enumerable, An Undecidable Problem That is RE, Undecidable Problems About Turing Machines, Post s Correspondence Problem, Other Undecidable Problems. CHAPTER - 10 : INTRACT CTABLE PROBLEMS The Classes P and NP, An NP Complete Problem, A Restricted Satisfiability Problem.

3 Contents iii automata, languages ages and computation FOR b.e. (o.u) Iii year i semester (COMMON TO CSE & IT) CONTENTS UNIT - I [CH. H. - 1] ] [AUTOMATA AUTOMATA] INTRODUCTION TO FINITE AUT UTOMA OMATA Structural Representations Automata and Complexity INDUCTIVE PROOFS Inductions on Integers THE CENTRAL CONCEPTS OF AUTOMA OMATA A THEORY Alphabets Strings The Empty String Length of String Powers of an Alphabet Concatenation of String Languages Solved Problems Expected University Questions with Answers UNIT - I [CH. - 2] ] [FINITE AUTOMATA] INTRODUCTION TO FINITE AUT UTOMA OMATA AN INFORMAL PICTURE OF FINITE AUTOMA OMATA DETERMINISTIC FINITE AUTOMA OMATA A (DFA) Definition of a Deterministic Finite Automaton How a DFA Processes Strings

4 iv Contents Simpler Notations for DFA s Transition Diagrams Transition Tables Extending the Transition Function to Strings The Language of a DFA Solved Problems NON-DETERMINISTIC FINITE AUTOMA OMATA A (NFA) A) An Informal View of NFA Definition of NFA The Extended Transition Function The Language of an NFA Equivalent of DFA A and NFA A Bad Case for the Subset Construction Differences between NFA A and DFA Solved Problems AN APPLICATION (TEXT SEARCH) Finding Strings in Text ext NFA A for Text ext Search A DFA A to Recognize a Set of Keywords Solved Problems FINITE AUT UTOMA OMATA A WITH EPSILON TRANSITIONS Uses of ε-transitions The Formal Notation for an ε-nf -NFA Epsilon Closures Extended Transitions and Languages for ε-nf -NFA s Eliminating ε-transitions Solved Problems Expected University Questions with Answers

5 Contents v UNIT - I [CH. H. - 3] ] [REGULAR EXPRESSIONS AND LANGUAGES] REGULAR EXPRESSIONS The Operators of Regular Expressions Building Regular Expressions Precedence of Regular Expression Operators Solved Problems FINITE AUTOMA OMATA A AND REGULAR EXPRESSIONS From DFA s to Regular Expressions Converting DFA s to Regular Expression by Eliminating States Converting Regular Expressions to Automata Solved Problems APPLICATIONS OF REGULAR EXPRESSIONS Regular Expressions in UNIX Lexical Analysis Finding Patterns in Text ext ALGEBRAIC LAWS FOR REGULAR EXPRESSIONS Associativity and Commutativity Identities and Annihilators Distributed Laws The Idempotent Law Laws Involving Closures Solved Problems Expected University Questions with Answers UNIT - II [CH. - 4] ] [PROPERTIES OF REGULAR LANGUAGES] PROPERTIES OF REGULAR LANGUAGES PROVING LANGUAGES GES NOT TO BE REGULAR The Pumping Lemma for Regular Languages Applications of the Pumping Lemma Solved Problems

6 vi Contents 4.3 CLOSURE PROPERTIES OF REGULAR LANGUAGES Closure of Regular Languages Under Boolean Operations Closure Under Union Closure Under Complementation Closure Under Intersection Closure Under Difference Reversal Homomorphisms Inverse Homomorphisms Solved Problems DECISION PROPERTIES OF REGULAR LANGUAGES Converting Among Representations Converting NFA s s to DFA s s DFA A to NFA A Conversion Automaton to Regular Expression Conversion Regular Expression to Automation Conversion Testing Empitness of Regular Languages Testing Membership in a Regular Language Solved Problems EQUIVALENCE AND MINIMIZATION OF AUTOMA OMATA Testing Equivalence of States Testing Equivalence of Regular Languages Minimization of DFA s Solved Problems Expected University Questions with Answers

7 Contents vii UNIT - II [CH. H. - 5] ] [CONTEXT FREE GRAMMARS AND LANGUAGES] CONTEXT FREE GRAMMARS An Informal Example Definition of Context Free Grammars Derivations Using a Grammar Leftmost and Rightmost Derivations The Language of Grammar Sentential Forms Solved Problems PARSE TREES Constructing Parse Trees The Yield of a Parse Tree ree Inference, Derivations and Parse Trees From Inferences to Trees From Trees to Derivations From Derivations to Recursive Inferences Solved Problems APPLICATIONS OF CONTEXT-FREE GRAMMARS Parsers The YACC Parser Generator Markup Languages XML and Document Type Definitions Solved Problem AMBIGUITY IN GRAMMARS AND LANGUAGES Ambiguous Grammars Removing Ambiguity From Grammars Inherent Ambiguity Solved Problems Expected University Questions with Answers

8 viii Contents UNIT - III [CH. H. - 6] ] [PUSHDOWN AUTOMATA] INTRODUCTION DEFINITION OF PUSHDOWN AUTOMA OMATA A (PDA) The Formal Definition of Pushdown Automata A Graphical Notation for PDA s Instantaneous Descriptions of a PDA THE LANGUAGES OF A PDA Acceptance Final State Accepting by Empty Stack From Empty Stack To o Final State From Final State to Empty Stack Solved Problems EQUIVALENCE OF PDA S S AND CFG S From Grammars to Pushdown Automata Procedure From PDA s s to Grammars Solved Problems DETERMINISTIC PUSHDOWN AUTOMA OMATA Definition of Deterministic PDA Regular Languages and Deterministic PDA s DPDA s and Context Free Languages DPDA s and Ambiguous Grammars Solved Problems Expected University Questions with Answers

9 Contents ix UNIT - III [CH. H. - 7] ] [PROPERTIES OF CONTEXT FREE LANGUAGES] NORMAL FORMS FOR CONTEXT FREE GRAMMARS Eliminating Useless Symbols Computing the Generating and Reachable Symbols Eliminating ε-productions Eliminating Unit Productions Chomsky Normal Form Reduction of CFG to CNF The Greibach Normal Form Conversion of CNF into GNF CNF Vs GNF Solved Problems PUMPING LEMMA FOR CONTEXT FREE LANGUAGES Statement of the Pumping Lemma OGDEN s Lemma Applications of Pumping Lemma Solved Problems CLOSURE PROPERTIES Substitution Applications of the Substitution Theorem Reversal Intersection With a Regular Language Inverse Homomorphism DECISION PROPERTIES OF CFL S S Testing Empitness of CFL s s Finiteness Testing Membership in a CFL Expected University Questions with Answers

10 x Contents UNIT - IV [CH. H. - 8] ] [INTRODUCTION TO TURING MACHINES] INTRODUCTION TO TURING MACHINES PROBLEMS THAT T COMPUTERS CANNOT SOLVE THE TURING MACHINE Turing Machine Model Transition Table Instantaneous Description (ID) For Turning Machines Acceptance of a Language by TM Construction of Turing Machine (TM) Transition Diagram for Turing Machine (TM) Turing Machines and Halting Solved Problems PROGRAMMING TECHNIQUES FOR TURING MACHINES Storage in the State Multiple Track rack Subroutines Solved Problems EXTENSIONS TO O THE TURING MACHINES Multi-Tape Turing Machines Equivalence of Single-Tape and Multi-Tape TM s Non-Deterministic Turing Machines RESTRICTED TURING MACHINES Turing Machine With Semi Infinite Tape ape Multistack Machines Counter Machines Off Line Turing Machine Linear Bounded Automata (LBA)

11 Contents xi 8.7 TURING MACHINE AND COMPUTERS Turing Machine as a Computer of Integer Functions unctions Solved Problems Turing Machine as a Generating Device Expected University Questions with Answers UNIT - V [CH. H. - 9] ] [UNDECIDABILITY UNDECIDABILITY] INTRODUCTION TO UNDECIDABILITY A LANGUAGE GE THAT T IS NOT RECURSIVELY ENUMERABLE Enumerating the Binary Strings Codes for Turing Machines The Diagonalization Language Proof That L d is Not Recursively Enumerable AN UNDECIDABLE PROBLEM THAT T IS RE Recursive Languages Complements of Recursive and R E Languages The Universal Language Undecidability of the Universal Language Halting Problem Reduction of Problems to Halting Problem of Turing Machine UNDECIDABLE PROBLEMS ABOUT TURING MACHINES Reduction Turing Machines That Accept the Empty Language Rice s Theorem and Properties of the RE Languages Problems About Turing Machine Specifications POST S CORRESPONDENCE PROBLEM (PCP) Definition of Post ost s Correspondence Problem roblem The Modified PCP Construction of PCP from MPCP Completion of the Proof of PCP Undecidability

12 xii Contents 9.6 OTHER UNDECIDABLE PROBLEMS Problems About Programs Undecidability of Ambiguity of CFG s The Complement of a List Language Expected University Questions with Answers UNIT - V [CH. H. - 10] ] [INTRACTABLE PROBLEMS] INTRODUCTION TO INTRACT CTABLE PROBLEMS THE CLASSES P AND NP Problems Solvable in Polynomial Time (P) An Example : Kruskal s Algorithm Non Deterministic Polynomial Time (NP) An NP : Problem : The Traveling Salesman Problem Polynomial Time Reductions eductions NP-Complete Problems NP-Hard AN NP COMPLETE PROBLEM The Satisfiability Problem Representing SAT T Instances Cook s s Theorem to Prove SAT T in NP Complete A RESTRICTED SATISFIABILITY PROBLEM Normal Forms for Boolean Expressions Converting Expressions to CNF (Reduction of SAT to CSAT) T) NP Completeness of CSAT NP Completeness of 3SAT Expected University Questions with Answers LATEST UNIVERSITY QUESTION PAPER [November/December ] [Main]... QP QP.4.4