NFA and DFA

Notre Dame University
Bangladesh
Submitted By:
Prapti Das – 201120008
Rup Chowdhury – 201120010
Submitted To:
A.H.M. Saiful Islam
Chairman, Department of CSE
Notre Dame University Bangladesh

NFA
“Non deterministic finite automata”

NFA
In NFA, for a particular input symbol, the machines
can move to any combination of the states in the
machine. In other words, the exact state to which the
machine moves cannot be determined. As it has finite
number of states, the machine is called Non-
deterministic Finite machine.

Formal Definition of an NFA
An NFA can be represented by a 5-tuple (Q, ∑, δ, q0, F) where −
•Q - is a finite set of states.
•∑ - is a finite set of symbols called the alphabets.
•δ - is the transition function where δ: Q × ∑ → 2Q
(Here the power set of Q (2Q) has been taken because in case of
NFA, from a state, transition can occur to any combination of Q
states)
•q0 is the initial state from where any input is processed (q0 ∈ Q).
•F is a set of final state/states of Q (F ⊆ Q).

Graphical Representation of an NFA
An NFA can be represented by digraphs called state
diagram. In which:
1.The state is represented by vertices.
2.The arc labeled with an input character
show the transitions.
3.The initial state is marked with an
arrow.
4.The final state is denoted by the double
circle

1.Q = {q0, q1, q2}
2.∑ = {0, 1}
3.q0 = {q0}
4.F = {q2}
Example 1:
Solution:
Transition diagram:

Transition Table:
In the above diagram, we can see that when the current state is
q0, on input 0, the next state will be q0 or q1, and on 1 input the
next state will be q1. When the current state is q1, on input 0 the
next state will be q2 and on 1 input, the next state will be q0.
When the current state is q2, on 0 input the next state is q2, and
on 1 input the next state will be q1 or q2.

DFA
“Deterministic finite automata”

DFA refers to deterministic finite automata.
Deterministic refers to the uniqueness of the
computation. The finite automata are called
deterministic finite automata if the machine is
read an input string one symbol at a time
DFA

Formal Definition of DFA
A DFA is a collection of 5-tuples same as we described in the
definition of NFA.
1.Q: finite set of states
2.∑: finite set of the input symbol
3.q0: initial state
4.F: final state
5.δ: Transition function
Transition function can be defined as:
1.δ: Q x ∑→Q

Graphical Representation of DFA
A DFA can be represented by digraphs called state
diagram. In which:
1.The state is represented by vertices.
2.The arc labeled with an input character show
the transitions.
3.The initial state is marked with an arrow.
4.The final state is denoted by a double circle.

Solution:
Transition Diagram:
Example 1:
1.Q = {q0, q1, q2}
2.∑ = {0, 1}
3.q0 = {q0}
4.F = {q2}

Difference between DFA and NFA :

Thank You
“Thank you, Everyone for being with us.”

NFA and DFA

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