A brief Introduction to CS6503 - THEORY OF COMPUTATION

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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