NFA Non Deterministic Finite Automata Definition

Definition Non Deterministic Finite Automata

A non-deterministic finite automaton (NDFA/NFA) is a 5-tuple (Q, Σ, δ, q0, F) 

where, 

Q = is a finite set of states. 

Σ = is a finite set of input symbols. 

δ = is a transition function mapping from Q × Σ to 2Q

q0 = is the initial state, q0 ∈ Q. 

F = is a set of final states, F ⊆ Q.

For example,

Consider the NFA that accepts all string ending with 01.

Transition Diagram

Transition Table

In this NFA, 

M = {Q, Σ, δ, q0, F} 

where, 

Q = {q0, q1, q2}. 

Σ = {0, 1}. 

δ = As shown above. 

q0 = Initial state. 

F = {q2}


Some terms in NFA:

Alphabet: An alphabet is a finite, non-empty set of symbols. 

Generally "Σ" is used to devote the alphabet. 

For example,

Σ = {0, 1} 

Σ = {a, b}

Symbol: Any character, number or special symbol can be treated as a "symbol". It is the member of the alphabet.

For example,

In above alphabet 0, 1 is symbol.

Word: A word or string is a finite sequence of symbols. 

For example,

S = 0110

S = ababa. 


To understood NDFA, lets compare it with DFA.

NDFA

DFA

Non Deterministic Finite Automata

Deterministic Finite Automata

Empty String transition allowed in DDFA.

Empty String transition not allowed in DFA.

In NDDFA, the next possible state is not determined.

In DFA, the next possible state is determined.

For NDFA, DFA may or may not exist.

For all DFA there exist NDFA

NDFA is like combination of many machines.

DFA is like a single machine.

NDFA is easy to construct.

DFA is touch to construct compare to NDFA.


Some examples of NDFA:

Problem 01: Construct a NDFA for the language accepting strings having even number of 1's over input alphabets ∑ = {0, 1}.



Problem 02: Construct a NDFA for the language accepting strings containg '01' as substring over input alphabets ∑ = {0, 1}.



Problem 03: Construct a NDFA for the language accepting strings containg '0' as divisible by 3 over input alphabets ∑ = {0, 1}.

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