Deterministic Finite Automaton

Finite Automaton can be classified into two types −

Deterministic Finite Automaton (DFA)

Non-deterministic Finite Automaton (NDFA / NFA)

Deterministic Finite Automaton (DFA)

In DFA, for each input symbol, one can determine the state to which the machine will move. Hence, it is called Deterministic Automaton. As it has a finite number of states, the machine is called Deterministic Finite Machine or Deterministic Finite Automaton.

Formal Definition of a DFA

A DFA 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 alphabet.

δ is the transition function where δ: Q × ∑ → Q

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 a DFA

A DFA 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 deterministic finite automaton be →

Q = {a, b, c},

∑ = {0, 1},

q₀ = {a},

F = {c}, and

Transition function δ as shown by the following table −

Its graphical representation would be as follows −