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A T CI
15CS54
Automata Theory And Computability
Subject Code: 15CS54
Hours/Week : 04
Total Hours : 50
Module I
I.A. Marks : 20
Exam Hours: 03
Exam Marks: 80
10 Hours
Why study the Theory of Computation, Languages and Strings:
Strings, Languages. A Language Hierarchy, Computation, Finite State Machines (FSM):
Deterministic FSM, Regular languages, Designing FSM, Nondeterministic FSMs, From FSMs
to Operational Systems, Simulators for FSMs, Minimizing FSMs, Canonical form of Regular
languages, Finite State Transducers, Bidirectional Transducers.
MO DUL E – 2
10Hours
MODULE – 3
10 Hours
MODULE – 4
10 Hours
MODULE – 5
1 0 Ho ur s
Regular Expressions (RE):
what is a RE?, Kleene’s theorem, Applications of REs, Manipulating and Simplifying REs.
Regular Grammars: Definition, Regular Grammars and Regular languages. Regular
Languages (RL) and Nonregular Languages: How many RLs, To show that a language is
regular, Closure properties of RLs, to show some languages are not RLs
Context-Free Grammars(CFG):
Introduction to Rewrite Systems and Grammars, CFGs and languages, designing CFGs,
simplifying CFGs, proving that a Grammar is correct, Derivation and Parse trees, Ambiguity,
Normal Forms. Pushdown Automata (PDA): Definition of non-deterministic PDA,
Deterministic and Non-deterministic PDAs, Non-determinism and Halting, alternative
equivalent definitions of a PDA, alternatives that are not equivalent to PDA.
Context-Free and Non-Context-Free Languages:
Where do the Context-Free Languages(CFL) fit, Showing a language is context-free,
Pumping theorem for CFL, Important closure properties of CFLs, Deterministic CFLs.
Algorithms and Decision Procedures for CFLs: Decidable questions, Un-decidable questions.
Turing Machine: Turing machine model, Representation, Language acceptability by TM,
design of TM, Techniques for TM construction
Variants of Turing Machines (TM), The model of Linear Bounded automata:
Decidability: Definition of an algorithm, decidability, decidable languages, 10 Hours
Undecidable languages, halting problem of TM, Post correspondence problem. Complexity:
Growth rate of functions, the classes of P and NP, Quantum Computation: quantum
computers, Church-Turing thesis.
Dept of CSE,SJBIT
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A T CI
15CS54
Text Books:
1. Elaine Rich: Automata, Computability and Complexity, 1st Edition, Pearson Education,
2012/13.
2. K.L.P. Mishra: Theory of Computer Science, Automata, Languages, and Computation,
3rd
Edition, PHI, 2012.
Reference Books:
1. John E Hopcroft, Rajeev Motwani, Jeffery D Ullman, Introduction to AutomataTheory,
Languages, and Computation, 3rd Edition, Pearson Education, 2013.
2. Michael Sipser : Introduction to the Theory of Computation, 3rd edition, Cengage
learning,2013
3. John C Martin, Introduction to Languages and The Theory of Computation, 3rd Edition,
Tata McGraw –Hill Publishing Company Limited, 2013 .
4. Peter Linz, “An Introduction to Formal Languages and Automata”, 3rd Edition, Narosa
Publishers, 1998.
5. Basavaraj S. Anami, Karibasappa K G, Formal Languages and Automata theory, Wiley
India, 2012 6. C K Nagpal, Formal Languages and Automata Theory, Oxford University
press, 2012.
Dept of CSE,SJBIT
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A T CI
15CS54
Table Of Contents
Page no
MODULE 1:INTRODUCTION TO FINITE AUTOMATA:
1
1.1: Introduction to finite Automata
1.2 : Central concepts of automata theory
1.3: Deterministic finite state machine
1.4:Non deterministic finite state machine
1.5 An application of finite automata
1.6 Finite automata with Epsilon transitions
1.7 Regular expressions
1.8 Finite automata and regular expressions
1.9 Applications of Regular expressions
MODULE - 2: PROPERTIES OF REGULAR LANGUAGES:
2.1 Regular languages
34
2.2 proving languages not to be regular languages
2.3 closure properties of regular languages
2.4 decision properties of regular languages
2.5 equivalence and minimization of automata
MODULE -3:Context Free Grammar and languages:
3.1 Context free grammars
53
3.2 parse trees
3.3 Applications
3.4 ambiguities in grammars and languages
Dept of CSE,SJBIT
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A T CI
15CS54
3.5: Definition of the pushdown automata
3.6: The languages of a PDA
3.7: Equivalence of PDA and CFG
3.8: Deterministic pushdown automata
MODULE-4: PROPERTIES OF CONTEXT FREE LANGUAGES
4.1 Normal forms for CFGS
74
4.2The pumping lemma for CFGS
4.3closure properties of CFLS
MODULE-5: INTRODUCTION TO TURING MACHINES
94
5.1 problems that computers cannot solve
5.2 The Turing machine
5.3 Programming techniques for turing machines
5.4 Extensions to the basic turing machines
5.5 Turing machines and computers
5.6: A language that is not recursively enumerable
5.7: a un-decidable problem that is RE
5.8: Posts correspondence problem
5.9: Other undecidable problem
Dept of CSE,SJBIT
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