Institute of Engineering & Management

Course:CS402 - Formal Language and Automata Theory PROGRAMME: COMPUTERSCIENCE&ENGINEERING COURSE: Formal Language and Automata Theory COURSECODE: CS402 COURSE AREA/DOMAIN: Theory of Computation

DEGREE:B. TECH SEMESTER: 46 CREDITS: 4 COURSE TYPE: Theory CONTACTHOURS: 4 (weekly)

CORRESPONDINGLABCOURSE CODE (IFANY): ---

LABCOURSE NAME: ---

Course pre-requisites CODE

COURSE NAME

DESCRIPTION

SEM

CS201

Basic Computation & Principles of Computer Programming Data structures and algorithms Discrete Mathematics

Programming basics

II

Concept of algorithms Elementary discrete mathematics including the notion of set, function, relation, product, partial order, equivalence relation, graph & tree. They should have a thorough understanding of the principle of mathematical induction.

III V

CS302 CS503

Course Objectives This course introduces the fundamental theory of computation. Starting with the most primitive computing device, a finite automaton, the course gradually introduces additional components to the device to enhance its computing power. The course also introduces students to the twin concepts of languages and grammars that correspond to classes of computing devices. Finally the course introduces the idea of a universal computing device and brings out theoretical limits of the very idea of computing.

Course Outcomes 1. To distinguish between computing and other kinds of machines. 2. To relate computing problems to machines, languages and grammars. 3. To construct regular expressions and grammars. 4. To design deterministic and nondeterministic automata, parsers and Turing machines. 5. To convert grammars to normal forms and eliminate ambiguities. 6. To recognize unsolvable problems and limitations of computing 7. To prove theorems by deduction, induction and contradiction. 8. Get familiarity with the seminal works of Turing, Godel and Chomsky.

Programme Outcomes addressed in this course a. b. c.

An ability to apply knowledge of mathematics, science, and engineering An ability to identify, formulate and solve engineering problems (e) An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice (k)

Department of CSE

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Institute of Engineering & Management Syllabus Module 1 UNIT DETAILS

I

Fundamentals: Basic definition of sequential circuit, block diagram, mathematical representation, concept of transition table and transition diagram (Relating of Automata concept to sequential circuit concept) Design of sequence detector, Introduction to finite state model

II Finite state machine: Definitions, capability & state equivalent, kth- equivalent concept III Merger graph, Merger table, Compatibility graph IV Finite memory definiteness, testing table & testing graph V Deterministic finite automaton and non deterministic finite automaton VI

Transition diagrams and Language recognizers.

Finite Automata: NFA with Î transitions - Significance, acceptance of languages. Conversions and Equivalence: Equivalence between NFA with and without Î transitions. NFA to VIII DFA conversion VII

HOURS

2 1 1 1 1 1 1 2

Minimization of FSM, Equivalence between two FSM’s , Limitations of FSM 1

IX X

Application of finite automata, Finite Automata with output- Moore & Mealy machine.

2

Module 2 UNIT DETAILS

I

Regular Languages: Regular sets.

HOURS

1

II Regular expressions, identity rules. Arden’s theorem state and prove

1

Constructing finite Automata for a given regular expressions, Regular string accepted by III NFA/DFA

1

IV Pumping lemma of regular sets. Closure properties of regular sets (proofs not required).

1

V Grammar Formalism: Regular grammars-right linear and left linear grammars. VI Equivalence between regular linear grammar and FA

1 1

VII Inter conversion, Context free grammar

1

Derivation trees, sentential forms. Right most and leftmost derivation of strings. (Concept VIII only)

1

Department of CSE

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Institute of Engineering & Management

Module 3 UNIT DETAILS

I

HOURS

Context Free Grammars, Ambiguity in context free grammars

1

II Minimization of Context Free Grammars. III Chomsky normal form and Greibach normal form

1

IV Pumping Lemma for Context Free Languages Enumeration of properties of CFL (proofs omitted). Closure property of CFL, Ogden’s V lemma & its applications VI Push Down Automata: Push down automata, definition.

1

1

1 1

Acceptance of CFL, Acceptance by final state and acceptance by empty state and its VII equivalence

1

VIII Equivalence of CFL and PDA, interconversion. (Proofs not required).

1

IX Introduction to DCFL and DPDA.

1

Module 4 UNIT DETAILS

I

Turing Machine : Turing Machine, definition, model

HOURS

1

II Design of TM, Computable functions III Church’s hypothesis, counter machine

1

IV Types of Turing machines (proofs not required) V Universal Turing Machine, Halting problem

1

Department of CSE

1 2

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Institute of Engineering & Management

Gaps in the syllabus - to meet industry/profession requirements S.NO.

1

DESCRIPTION

How to apply machine models in designing programming logic

PROPOSED PO ACTIONS MAPPING b Lab

Topics beyond syllabus/advanced topics S.NO.

DESCRIPTION

1

.

HOURS

Web Source References S.NO.

URL

1

Delivery/Instructional Methodologies S.NO.

DESCRIPTION

1

Chalk and Talk

2

Study Material

Assessment Methodologies S.NO.

DESCRIPTION

TYPE

2

Student Assignment . Tests

3

University Examination

Direct

4

Student Feedback

Indirect

1

Department of CSE

Direct Direct

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Institute of Engineering & Management

Course Plan S. NO.

Day

Module

1.

Day 1

2.

Day 2

3.

Day 3

4.

Day 4

5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

Day 5

Day 20 Day 21

22.

Day 22

23. 24. 25. 26. 27. 28. 29. 30.

Day 23 Day 24

IX

Day 25 Day 26 Day 27 Day 28 Day 29

X

I

II

Day 6 Day 7 Day 8 Day 9 Day 10 Day 11 Day 12 Day 13 Day 14 Day 15 Day 16 Day 17 Day 18 Day 19

Day 30

Department of CSE

IV

V

VI

VII

VIII

Topic Need for this subject, Decision making as computation Concept of sequential circuit Flip Flop and concept of memory Definition of Finite State Automaton Transition table and diagram, Mathematical representation Worked out examples Definition of language and grammar Rules – single symbol, concatenation, union, Kleene Closure Closure properties Worked out examples Definition, Conversion from NFA to DFA Worked out examples Introduction, Equivalent States, Distinguished State Myhill-Nerode Theorem Table filling method with worked out example Partitioning method with worked out example Arden’s Theorem Worked out example Limitations of Finite State Machines Pumping Lemma for Regular Language Worked out examples Revisiting Formal Grammar, Generalization of grammar with increased power Introduction to Context Free Grammar and Context Free Language Mathematical Definition of Context Free Language Closure properties of Context Free Language Normal forms – Chomsky and Greibach Normal Form Worked out examples Limitations of Context Free Language Pumping Lemma for Context Free Language Worked out examples

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