Deterministic Finite Automaton


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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 −

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

Its graphical representation would be as follows −

DFA Graphical Representation

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