Theory of Computation

Section A

Nondeterministic Finite Automaton

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 → 2 Q (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}

The transition function d as shown below:

Present State	Next State for  Input 0	Next State for Input 1
a	a,b	b
b	c	a,c
b	b,c	c

Its graphical representation would be as follows:

NFA Representation