This document outlines the course objectives and units for a Theory of Computation course. The course covers various computing models like finite state machines, pushdown automata, and Turing machines. It examines decidability and undecidability of problems. Key topics include regular languages and expressions, context-free grammars, pumping lemmas, Turing machines, and analyzing complexity classes like P and NP-complete problems. The course aims to help students understand these foundational models of computation and analyze problem solvability.

1. CS6503 THEORY OF COMPUTATION L T P C 3 0 0 3
OBJECTIVES:
The student should be made to:
 Understand various Computing models like Finite State Machine, Pushdown Automata, and
Turing Machine.
 Be aware of Decidability and Un-decidability of various problems.
 Learn types of grammars.
UNIT I FINITE AUTOMATA 9
Introduction- Basic Mathematical Notation and techniques- Finite State systems – Basic Definitions –
Finite Automaton – DFA & NDFA – Finite Automaton with €- moves – Regular Languages- Regular
Expression – Equivalence of NFA and DFA – Equivalence of NDFA’s with and without € - moves –
Equivalence of finite Automaton and regular expressions –Minimization of DFA- - Pumping Lemma
for Regular sets – Problems based on Pumping Lemma.
UNIT II GRAMMARS 9
Grammar Introduction– Types of Grammar - Context Free Grammars and Languages– Derivations
and Languages – Ambiguity- Relationship between derivation and derivation trees – Simplification of
CFG – Elimination of Useless symbols - Unit productions - Null productions – Greiback Normal form
– Chomsky normal form – Problems related to CNF and GNF.
UNIT III PUSHDOWN AUTOMATA 9
Pushdown Automata- Definitions – Moves – Instantaneous descriptions – Deterministic pushdown
automata – Equivalence of Pushdown automata and CFL - pumping lemma for CFL – problems
based on pumping Lemma.
UNIT IV TURING MACHINES 9
Definitions of Turing machines – Models – Computable languages and functions –Techniques for
Turing machine construction – Multi head and Multi tape Turing Machines - The Halting problem –
Partial Solvability – Problems about Turing machine- Chomskian hierarchy of languages.
UNIT V UNSOLVABLE PROBLEMS AND COMPUTABLE FUNCTIONS 9
Unsolvable Problems and Computable Functions – Primitive recursive functions – Recursive and
recursively enumerable languages – Universal Turing machine. MEASURING AND CLASSIFYING
COMPLEXITY: Tractable and Intractable problems- Tractable and possibly intractable problems – P
and NP completeness - Polynomial time reductions.
TOTAL: 45 PERIODS
OUTCOMES:
At the end of the course, the student should be able to:
 Design Finite State Machine, Pushdown Automata, and Turing Machine.
 Explain the Decidability or Undecidability of various problems
TEXT BOOKS:
1. Hopcroft J.E., Motwani R. and Ullman J.D, “Introduction to Automata Theory, Languages
and Computations”, Second Edition, Pearson Education, 2008. (UNIT 1,2,3)
2. John C Martin, “Introduction to Languages and the Theory of Computation”, Third Edition,
Tata McGraw Hill Publishing Company, New Delhi, 2007. (UNIT 4,5)
REFERENCES:
1. Mishra K L P and Chandrasekaran N, “Theory of Computer Science - Automata, Languages
and Computation”, Third Edition, Prentice Hall of India, 2004.
2. Harry R Lewis and Christos H Papadimitriou, “Elements of the Theory of Computation”,
Second Edition, Prentice Hall of India, Pearson Education, New Delhi, 2003.
3. Peter Linz, “An Introduction to Formal Language and Automata”, Third Edition, Narosa
Publishers, New Delhi, 2002.
4. Kamala Krithivasan and Rama. R, “Introduction to Formal Languages, Automata Theory and
Computation”, Pearson Education 2009

2. UNIT I FINITE AUTOMATA
Introduction
Basic Mathematical Notation and techniques
Finite State systems
Basic Definitions
Finite Automaton
DFA & NDFA
Finite Automaton with ε- moves
Regular Languages
Regular Expression
Equivalence of NFA and DFA
Equivalence of NDFA’s with and without ε - moves
Equivalence of finite Automaton and regular expressions
Minimization of DFA
Pumping Lemma for Regular sets
Problems based on Pumping Lemma
UNIT II GRAMMARS
Grammar Introduction
Types of Grammar
Context Free Grammars and Languages
Derivations and Languages
Ambiguity
Relationship between derivation and derivation trees
Simplification of CFG
Elimination of Useless symbols
Unit productions
Null productions
Greiback Normal form
Chomsky normal form
Problems related to CNF and GNF
UNIT III PUSHDOWN AUTOMATA
Pushdown Automata
Definitions
Moves
Instantaneous descriptions
Deterministic pushdown automata
Equivalence of Pushdown automata and CFL
Pumping lemma for CFL
Problems based on pumping Lemma.

3. UNIT IV TURING MACHINES
Definitions of Turing machines
Models
Computable languages and functions
Techniques for Turing machine construction
Multi head and Multi tape Turing Machines
The Halting problem
Partial Solvability
Problems about Turing machine
Chomskian hierarchy of languages
UNIT V UNSOLVABLE PROBLEMS AND COMPUTABLE FUNCTIONS
Unsolvable Problems and Computable Functions
Primitive recursive functions
Recursive and recursively enumerable languages
Universal Turing machine.
MEASURING AND CLASSIFYING COMPLEXITY:
Tractable and Intractable problems
Tractable and possibly intractable problems
P and NP completeness
Polynomial time reductions.

4. UNIT I FINITE AUTOMATA
1.1 Introduction
1.2 Basic Mathematical Notation and techniques
1.3 Finite State systems
1.4 Basic Definitions
1.5 Finite Automaton
1.6 DFA & NDFA
1.7 Finite Automaton with ε- moves
1.8 Regular Languages
1.9 Regular Expression
1.10 Equivalence of NFA and DFA
1.11 Equivalence of NDFA’s with and without ε - moves
1.12 Equivalence of finite Automaton and regular expressions
1.13 Minimization of DFA
1.14 Pumping Lemma for Regular sets
1.15 Problems based on Pumping Lemma
UNIT II GRAMMARS
2.1 Grammar Introduction
2.2 Types of Grammar
2.3 Context Free Grammars and Languages
2.4 Derivations and Languages
2.5 Ambiguity
2.6 Relationship between derivation and derivation trees
2.7 Simplification of CFG
2.8 Elimination of Useless symbols
2.9 Unit productions
2.10 Null productions
2.11 Greiback Normal form
2.12 Chomsky normal form
2.13 Problems related to CNF and GNF
UNIT III PUSHDOWN AUTOMATA
3.1 Pushdown Automata
3.2 Definitions
3.3 Moves
3.4 Instantaneous descriptions
3.5 Deterministic pushdown automata
3.6 Equivalence of Pushdown automata and CFL
3.7 Pumping lemma for CFL
3.8 Problems based on pumping Lemma.

5. UNIT IV TURING MACHINES
4.1 Definitions of Turing machines
4.2 Models
4.3 Computable languages and functions
4.4 Techniques for Turing machine construction
4.5 Multi head and Multi tape Turing Machines
4.6 The Halting problem
4.7 Partial Solvability
4.8 Problems about Turing machine
4.9 Chomskian hierarchy of languages
UNIT V UNSOLVABLE PROBLEMS AND COMPUTABLE FUNCTIONS
5.1 Unsolvable Problems and Computable Functions
5.2 Primitive recursive functions
5.3 Recursive and recursively enumerable languages
5.4 Universal Turing machine.
5.5 MEASURING AND CLASSIFYING COMPLEXITY:
5.6 Tractable and Intractable problems
5.7 Tractable and possibly intractable problems
5.8 P and NP completeness
5.9 Polynomial time reductions.