The document provides an introduction to the theory of computation. It discusses how the theory of computation deals with how efficiently problems can be solved using algorithms on computational models. The field is divided into three main branches: automata theory and language, computability theory, and computational complexity theory. The objectives of the course are to understand computational models like finite state machines, pushdown automata, and Turing machines, and to learn about the decidability and undecidability of problems. The course will cover topics like finite automata, grammars, pushdown automata, Turing machines, unsolvable problems, and computational complexity.

1. Introduction to
THEORY OF
COMPUTATION
-Sampath Kumar S,
AP/CSE, SECE

2. THEORY OF COMPUTATION
 In theoretical computer science and
mathematics, the theory of computation is the
branch that deals with how efficiently
problems can be solved on a model of
computation, using an algorithm.
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3. THEORY OF COMPUTATION
 Computation: Task performed by ‘calculator’
or ‘computer’ or a ‘machine’.
 Theory: What is the theory behind about this
machine
 Capabilities of the machine
 Problems that could be solved by this machine
 Limitations of this machine
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4. Branches of ToC
The field is divided into three major branches:
1. Automata theory and language
2. Computability theory
3. Computational complexity theory
which are linked by the question: "What are
the fundamental capabilities and
limitations of computers?“.
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5. OBJECTIVES of this
course:
 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.
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6. UNIT I: FINITE AUTOMATA
 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.
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7. 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.
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8. 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.
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9. 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.
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10. 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.
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11. OUTCOMES:
 Design Finite State Machine, Pushdown
Automata, and Turing Machine.
 Explain the Decidability or Undecidability of
various problems
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12. Applications of ToC
 Artificial Intelligence
 Compiler Design
 Robotics
 Circuit Design
 Natural Language Processing
 Knowledge based System
 Quantum Computing
 Pattern Recognition
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14. நன்றி
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