NFA Non Deterministic Finite Automata by Mudasir khushik

Presentation Topic
NFA
Non Deterministic Finite Automata

Definition:
NFA (Non Deterministic Finite Automaton)
In NFA the exact state to which the machine
moves cannot be determined it is called
NFA.
As it has finite number of states the
machine is called Non Deterministic Finite
Machine or Non Deterministic Finite
Automaton.

NFA is represented by 5 tuples:
(Q , ∑ , ∂ , qo , F)
Q = finite set of states
∑ = finite set of input symbols
∂ = Transition Function
qo = initial state
F = final state

NFA example:
if ∑ = {0,1}
input string 011
NFA:
P q
1
0,1
+

Transition Table:
P q
1
0,1
Input 0 1
p {p} {p,q}
q {^} {^}
+

Transition Function:
input string 011
∂ (p,0)=p
∂ (p,1)=(p,q)
∂(q,1)=
^
P q
1
0,1
+

Before Jumping to NFA lets have an Eye on
following Things.
Alphabets
Rules
Descriptive
Method
Regular
Expression
Language
F.A
String

In Automata we deal with Language:
Language is the Combination of:
Alphabets
∑
Rules

Example:
if ∑ = {a , b} => (Alphabets)
All Strings which end with a.(RULE)
String: is a finite sequence of symbols
taken from Alphabets.
Difference between String and words.
Length of a String:
length of a string is always positive.

Example:
String = abba (length = 4)
String = abaaaba (length = 7)
Concatenation of String:
when two or more strings combine to form a new
string.
If x=ab
y=c
Reverse of String:
if w= abc
then find reverse of string
if q= stwm
find reverse of string?

If ∑ = {aa, bab} find the length and reverse
of the following string.
W = babaabab
Tocanisation :
(bab)(aa)(bab)
Reverse of the String:
Palindrome

Ways to Represent Language in Automata:
Descriptive
Method
R.E
Regular Expression
F.A
N.F.A D.F.A

1:Descriptive Method
if ∑ = {a,b}
all strings ending with a
{a, ba, aa, aaa, aba, …} => infinite
{a, aba, ba, aaa, aa …} => Wrong
order of string must be ascending.

Descriptive Method Examples:
1: if ∑ = {0,1}
write all string which contain 00.
2: if ∑ = {a,b}
write all string which starts with a.
3:if ∑ = {0,1}
write all possible strings of even length.
4:if ∑ = {a,b}
write all possible strings that contain ab.
{ab, aab, abb, bab…}

Regular Expression:
why we use Regular Expression
Because descriptive method se language ke
saray words nai likhay ja sakte.
Example:
if ∑ = {a,b}
all strings which starts with a.
D.M={a, aa, ab, aaa, aab, aba, abb…}
R.E=?

Regular Expression Language:
Single letter
Language
Finite Language Infinite Language
Kleene Closure Positive Closure

1: Single letter Language:
The language in which there is only one
Alphabet.
Example
if ∑ = {a} R.E = a
if ∑ = {b} R.E = b
2: Finite Language: The language whose string
is countable.
Example: if ∑ = {a,b}
all string of length two
{aa, bb, ab, ba}
R.E= ?

Infinite Language: The Language whose
string is uncountable.
Two types of properties
1: Kleene Closure: *, ^, e.g: if ∑={a} Make
All strings. R.E=?
2: Positive Closure: +, do not contain ^
value e.g: if ∑ = {a} Make all Strings.
R.E=?

Examples Of Regular Expression:
1: if ∑ ={a} write R.E function for all strings
{^,a,aa,aaa,aaaa…}
R.E=?
2:if ∑ = {a} write R.E for all strings without null
^.
{a,aa,aaa,aaaa…}
R.E=?
3:if ∑ ={a,b} write R.E for all possible strings.
{^,a,b,ab,ba,aab,abb,aaa…}
R.E=?

+ Symbol in R.E:
If R.E = (a+b) then what does it mean?
It means at a time we can select one value either
from right side or from the left side.
Possible strings for (a+b) will be:
strings = a,b
lets have an example:
if ∑ ={a,b} write possible strings whose length is 3.
R.E= (a+b)(a+b)(a+b)
if ∑ ={a,b} write all possible strings whose 3rd letter is
a.
R.E=?

If ∑ ={a,b} write R.E for the string {ab,ba,aab}
hint: it’s a finite language
R.E=?
If ∑ ={a,b} write all possible strings that starts and end with b.
{bb,bab,baab,babb…}
R.E=?
Hint: We always complete our condition first
if ∑ ={a,b} write all possible strings that starts and end with
same letter.
If ∑ ={a,b} write all possible strings that contain exactly two
times a in a string.
Strings:{aa,aab,abab,baba,babab…}
R.E=?

F.A:
why we use Finite Automata if we already have two
methods to represent the language.
We use finite automata because it is the
diagrammatically representation of the language.
Diagrams are easy to understand.
Different names of F.A:
Machine/F.A/F.S.M/D.F.M/D.F.A
F.S.M: finite state machine
D.F.M: deterministic finite machine
D.F.A: deterministic finite automata

Types of Finite Automata:
N.F.A
Non
Deterministic
Finite Automata
D.F.A
Deterministic
Finite Automata

Basics of N.F.A
States
1:Initial State
The F.A can only have single initial state.
The F.A always starts from initial state.
2:Final State: It is the place where diagram can stop.
F.A has minimum 1 and maximum more than 1 no of final states , but
not infinite.
3:Normal State: From this state, diagram can not stop neither start.
-
+

N.F.A with Examples:
1: R.E=a draw N.F.A
2:R.E= a+b draw N.F.A
Routes are known as transition.
3:R.E = ab

N.F.A with Examples:
Lets move to some difficult ones.
4: if ∑ ={a,b} All string that end with a. R.E=?
N.F.A Techniques.
5:if ∑={a} for all strings R.E=?
6:if ∑={a,b} for all strings R.E=?
7:if ∑={a,b} for all strings that starts with a and end with bb.
R.E technique + N.F.A technique. R.E=?
8:if ∑={a,b} for all possible strings that starts and end with
same letter. R.E=?
R.E= two cases
compare its N.F.A with D.F.A
9:if ∑={a,b} for all strings that starts and end with
different letter. R.E=?

10:if ∑={a,b} for all strings that contain
double a toghether.
11: if ∑={a} for all string of even length.
{^,aa,aaaa,aaaaaa,…}
12: if ∑={a,b} strings of length two.
R.E= (a+b)(a+b)

Thanks
A presentation by
Mudasir Khushik
Batch:2k16
University of Sindh Campus At
Thatta

NFA Non Deterministic Finite Automata by Mudasir khushik

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