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, nay number of 1’s can be present here and for this put self-loop of ‘1’ on initial state “A”.
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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 DFAimport java.util.*;class GFG{ // Function for the state Astatic 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 Bstatic 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 Cstatic 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 codepublic 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 DFAdef 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 inputn = input()# call checkStateA# to check the inputted stringcheckStateA(n) |
C#
// C# code for the above DFAusing System;using System.Collections;using System.Collections.Generic;class GFG{ // Function for the state Astatic 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 Bstatic 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 Cstatic 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 codepublic 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 |
