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.


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 StateNext State for Input 0Next State for Input 1

Its graphical representation would be as follows −

DFA Graphical Representation


Related Posts

Comments are closed.

© 2024 Software Engineering - Theme by WPEnjoy · Powered by WordPress