A nondeterministic finite automaton, or nondeterministic finite-state machine, is a finite-state machine that does not need to obey the restrictions set by DFA, where each of the transition is uniquely determined by its source state and input symbol, and reading an input symbol is required for each state transition.
Formal Definition of an NDFA
An NDFA 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 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.
