This document provides an introduction and overview of the Theory of Computation course BCSE304L. It discusses what computation and computers are from an abstract, theoretical perspective. Computation is defined as an effective method that can solve problems with a finite number of inputs and outputs. Computers are physically realizable machines that can perform computation. The Theory of Computation studies what problems can and cannot be solved by computers based on their physical limitations. The course will cover automata theory including finite automata, context-free grammars, and Turing machines. It will examine formal language classes and their relationships. Students will learn to design grammars and recognizers, prove theorems, and determine decidability of problems. The course is divided

1. BCSE304L-THEORY OF
COMPUTATION
Introduction
Dr. R. Jothi

2. Outline
• Course Introduction
• Why this course
• Course outcomes
• Course organization

3. What is Computation?
• Computation is an effective method (an Algorithm!), which given a
problem with possibly a finite number of inputs, can produce an
output which can be recognized as a solution to the problem.
• 'Effective method' is here used in the rather special sense of a
method each step of which is precisely predetermined and which is
certain to produce the answer in a finite number of steps.

4. What is a Computer?
• A Computer is a physically realizable machine which can perform
computation.
• A Computer is a Formal System (abstract model). This is a direct
implication of the requirement that each step in an “Effective
Method” is precisely predetermined

5. What is Theory of Computation?
• It is the study about the ultimate capability of Computers, that is
what problems can be computed, what cannot and what can only
be solved partially by any computer which works under the
limitation of being “physically realizable” and employing only
“Effective Methods”.
• This requires working with abstract models of computers /
computation and as we will show, this has more to do with the
nature of problems rather than computers.

6. Why should I learn TOC?
• State machines
• Regular expressions
• Grammars

7. Why should I learn TOC?
• State machines
start
start
end
A formal system is one of several possible states. Every input or
stimulus causes a change of state

8. Why should I learn TOC?
• Regular expressions

9. Why should I learn TOC?
• Grammar
• Compiler Design
• Parsing

10. What is Automata?
• Automata theory is the study of abstract machines and automata, as
well as the computational problems that can be solved using them. It
is a theory in theoretical computer science.

11. • Theoretical developments bear directly on what computer scientists
do today
• Finite automata, formal grammars: design/ construction of software
• Turing machines: help us understand what we can expect from a
software
• Theory of intractable problems: are we likely to be able to write a
program to solve a given problem? Or we should try an
approximation, a heuristic...

12. Applications
• Compiler Design
• Natural language processing
• Speech recognition
• Search engines (finding text pattern in web pages)
• Networking protocols
• VLSI design

13. Course Objectives
• Study concepts in automata theory
• Identify different formal language classes and their relationships
• Design grammars and recognizers for different formal languages
• Prove or disprove theorems in automata theory using its properties
• Determine the decidability and intractability of computational
problems

14. Course Organization
• Very broadly, the course will contain three parts:
• Part I) Regular languages : DFA, NFA
• Part II)Context-free languages : PDA
• Part III)Recursively enumerable languages : Turing machines & decidability

15. Text book
• Introduction to Automata Theory, Languages and Computation
• By J.E. Hopcroft, R. Motwani, J.D. Ullman
• 3rd Edition
• Addison Wesley/Pearson