TOC Non-deterministic Finite Automaton (NDFA)

In NDFA, for a particular input symbol, the machine 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. Hence, it is called Non-deterministic Automaton. As it has finite number
of states, the machine is called Non-deterministic Finite Machine or Nondeterministic
Finite Automaton.

Formal Definition of an NDFA
An NDFA can be represented by a 5-tuple (Q, Σ, δ, q0, F) where:
 Q is a finite set of states.
 Σ is a finite set of symbols called the alphabets.
 δ is the transition function where δ: Q × Σ → 2Q
(Here the power set of Q (2Q) has been taken because in case of NDFA, 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 NDFA: (same as DFA)
An NDFA is represented by digraphs called state diagram.
 The vertices represent the states.
 The arcs labeled with an input alphabet show the transitions.
 The initial state is denoted by an empty single incoming arc.
 The final state is indicated by double circles.

Example
Let a non-deterministic finite automaton be ->
 Q = {a, b, c}
 Σ = {0, 1}
 q0 = {a}
 F={c}