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 2^Q. 
• q0 = is the initial state, q0 ∈ Q. 
• F = is a set of final states, F ⊆ Q.

Reference: Introduction to the Theory of Computation” by Michael Sipser

Example of NFA,

Consider the NFA that accepts all string ending with 01.

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}

Reference:

• Introduction to the Theory of Computation” by Michael Sipser.