DFA that recognizes number of 0 is multiple of 3 on input {0,1}

Finite Automata is known as a finite state machine that are acceptable otherwise not acceptable. on the input alphabet ‘0’ and 1′.

• Determine the initial state.
• The transition occurs on every input alphabet.
• Determine whether the self-loop should apply or not.
• Mark’s final state.

Designing DFA step by step :
Step-1:
Make initial state “A” then it is the possibility that there would not be any ‘0’ but have only ‘1’ in the string which is acceptable because 0 is divisible by 3.So, in this case, any number of 1’s can be present here and for this put self-loop of ‘1’ on initial state “A”.

Step-2:
Create transition of input alphabet ‘0’ from state “A” to state “B”.

Step-3:
After one ‘0’ any number of 1’s can be present i.e, no ‘1’ or more than one ‘1’.For this put self loop of ‘1’ on state “B”.

Step-4:
Now create transition of input alphabet ‘0’ from state “B” to state “C” and after two 0’s any number of 1’s can be found in the string and for this put self loop of ‘1’ on initial state “C”.

Step-5:
Before transition of third ‘0’ we need to think about the logic so that after this transition the machine will accept string that have number of zeros divisible by 3.For this transit ‘o’ from state “C” to state “A”.AS third zero is reaching to state “A” so make state “A” be final state.

Transition table of above DFA:

States	Input (0)	Input (1)
—> A *	B	A
B	C	B
C	A	C

In above table, —> represents initial state and * represents final state. In this article, initial and final state is same which is final state.
Transition rules of above DFA: 

Implementing :

Java

// Java code for the above DFA
import java.util.*;

class GFG{

// Function for the state A
static void checkStateA(String n)
{

    // Check length of n
    // is 0 then print
    // String accepted
    if (n.length() == 0)
        System.out.print("String accepted");

    // If 1 is found call function
    // checkStateA otherwise if 0
    // is found call function stateB
    else
    {
        if (n.charAt(0) == '1')
            checkStateA(n.substring(1));
        else
            stateB(n.substring(1));
    }
}

// Function for the state B
static void stateB(String n)
{

    // Check length of n
    // is 0 then print
    // String not accepted
    if (n.length() == 0)
        System.out.print("String not accepted");

    // If 1 is found call function
    // stateB otherwise if 0
    // is found call function stateC
    else
    {
        if (n.charAt(0) == '1')
            stateB(n.substring(1));
        else
            stateC(n.substring(1));
    }
}

// Function for the state C
static void stateC(String n)
{

    // Check length of n
    // is 0 then print
    // String not accepted
    if (n.length() == 0)
        System.out.print("String not accepted");

    // If 1 is found call function
    // stateC otherwise if 0
    // is found call function checkStateA
    else
    {
        if (n.charAt(0) == '1')
            stateC(n.substring(1));
        else
            checkStateA(n.substring(1));
    }
}

// Driver code
public static void main(String []args)
{
    Scanner sc = new Scanner(System.in);

    // Take String input
    String n = sc.nextLine();

    // Call checkStateA to
    // check the inputted String
    checkStateA(n);
}
}

// This code is contributed by pratham76

Python3

# Python3 code for the above DFA
def checkStateA(n):

    # check length of n
    # is 0 then print
    # string accepted
    if(len(n)== 0):
        print("string accepted")

    # if 1 is found call function
    # checkStateA otherwise if 0
    # is found call function stateB
    else:
        if(n[0]=='1'):
            checkStateA(n[1:])
        else:
            stateB(n[1:])


def stateB(n):

    # check length of n
    # is 0 then print
    # string not accepted
    if(len(n)== 0):
        print("string not accepted")

    # if 1 is found call function
    # stateB otherwise if 0
    # is found call function stateC
    else:
        if(n[0]=='1'):
            stateB(n[1:])
        else:
            stateC(n[1:])


def stateC(n):

    # check length of n
    # is 0 then print
    # string not accepted
    if(len(n)== 0):
        print("string not accepted")

    # if 1 is found call function
    # stateC otherwise if 0
    # is found call function checkStateA
    else:
        if(n[0]=='1'):
            stateC(n[1:])
        else:
            checkStateA(n[1:])

# take string input
n = input()

# call checkStateA
# to check the inputted string
checkStateA(n)

C#

// C# code for the above DFA
using System;
using System.Collections;
using System.Collections.Generic;
class GFG{

// Function for the state A
static void checkStateA(string n)
{
  // check length of n
  // is 0 then print
  // string accepted
  if(n.Length == 0)
    Console.Write("string accepted");

  // if 1 is found call function
  // checkStateA otherwise if 0
  // is found call function stateB
  else
  {
    if(n[0] == '1')
      checkStateA(n.Substring(1));
    else
      stateB(n.Substring(1));
  }
}

// Function for the state B
static void stateB(string n)
{
  // check length of n
  // is 0 then print
  // string not accepted
  if(n.Length == 0)
    Console.Write("string not accepted");

  // if 1 is found call function
  // stateB otherwise if 0
  // is found call function stateC
  else{
    if(n[0] == '1')
      stateB(n.Substring(1));
    else
      stateC(n.Substring(1));
  }
}

// Function for the state C
static void stateC(string n)
{
  // check length of n
  // is 0 then print
  // string not accepted
  if(n.Length == 0)
    Console.Write("string not accepted");

  // if 1 is found call function
  // stateC otherwise if 0
  // is found call function checkStateA
  else
  {
    if(n[0] == '1')
      stateC(n.Substring(1));
    else
      checkStateA(n.Substring(1));
  }
}

// Driver code
public static void Main(string []args)
{
  // take string input
  string n = Console.ReadLine();

  // call checkStateA
  // to check the inputted string
  checkStateA(n);
}
}

// This code is contributed by rutvik_56

Time complexity: O(n) where n given string input

Auxiliary space: O(1)