AUTOMATA THEORY
Reference
Introduction to Automata Theory Languages and Computation
Hopcraft, Ullman and Motwani
Automata Theory
Automata theory is the abstract computing device or
machine.
Finite automata involves states and transitions among
states in response to inputs.
Finites automata are a useful model for many important
kinds of h/w and s/w.
Why Study Automata Theory?
 There are several reasons why the study of automata
and complexity is an important part of the core of
Computer science.
Why Study Automata Theory?
Some of the most important kinds :
1.
Software for designing and checking the behavior of
digital circuits.
2.
The “lexical analyzer” of a typical compiler, that is, the
compiler component that breaks the input text into
logical units, such as identifiers, keywords and
punctuations.
Why Study Automata Theory?
3. Software for scanning large bodies of text, such as
collections of web pages, to find occurrences of words,
phrases, or other patterns.
4. Software for verifying systems of all types that have a finite
number of distinct states, such as communications
protocols
or
information.
protocols
for
secure
exchange
of
A finite automata modeling on/off
switch
push
start
on
off
push
The devices remember whether it is in the “on” state or
“off” state and it allows the user to press a button whose
effect is different.
A finite automata modeling on/off
switch
The states are represented by circles, In this example two
states “on” and “off”.
One of the states is designated by the start states.
It is often necessary to indicate one or more states as “final”
or “accepting” states.
A finite Automation modeling
recognition of then
start
t
t
h
th
e
n
the
then
 This figure shows finite automation that could be part of a
lexical analyzer. The job of this automation is to recognize the
keyword then.
Introduction to Finite Automata
 A finite Automation has a set of states and its control moves
from one state to another in response to external inputs.
 One of the crucial distinction among classes of finite automata
is whether that control is “deterministic” meaning that the
automation cannot be in more than one state at one time or
“nondeterministic” meaning that it may be in several states at
one.
Automata and Complexity
Automata and Complexity
What can a computer do? -- Computability:
Studying problems which can be solved by computer,
called decidable problems.
Decidability is the main topic in computability.
Automata and Complexity
 Automata and Complexity
 What can a computer do efficiently? ---
 Computational Complexity:
 Studying tractable problems solvable with some slowly growing
function (like polynomial) of input size, & intractable problems solvable
with fast growing function (like exponential).
 Intractability is the main topic of computational complexity.
Central Concepts of Automata
Theory
Three basic concepts
Alphabet --- a set of symbols
Strings --- a sequence of symbols from an
alphabet
Language --- a set of strings from the same
alphabet
Central Concepts of Automata
Theory
Alphabets :

finite, nonempty set of symbols.

Conventional notation --- S

Ex: 1. ∑ = {0,1} the binary alphabet,

2. ∑ = {a, b, c, . . . z}

3. The set of all ASCII characters
Contd.
Strings:

finite sequences of symbols chosen from some
alphabet

Ex: 01101 is string from the binary alphabet ∑ = {0,1} .
Empty string e --- a string with zero occurrences of
symbols
Length |w| of string w --- the number of positions for
symbols in w
Examples --- |0111|=4, |e|=0, …
Central Concepts of Automata
Theory
 Powers of an Alphabets:
∑º={€}
∑1={0,1}
∑2={00,01,10,11}
∑3={000,001,010,011,100,101,110,111}
Central Concepts of Automata
Theory

Language:
A language is set of strings all of which chosen from ∑* .
Example:
1. The language of all strings consisting of n 0’s followed by
n 1’s:
{€,01,0011,000111,…..}
Central Concepts of Automata
Theory
2.
The set of strings of 0’s and 1’s with an equal number
each:
{€,01,10,0011,0101,1001…..}
3.
The set of binary number whose value is prime:
{10,11,101,111,1011,…..}
Central Concepts of Automata
Theory
 Problem:
 In automata theory, a problem is the question
of deciding whether a given string is a member
of some particular language.
End of Class