Design a DFA that accepts a string containing 3 a’s and 3 b’s

Problem Statement: Design a Definite Finite Automata for accepting the permutation of Three a’s and Three b’s over the input {a, b} 

Input: S = “aaabbb” 
Output: Accepted 
Explanation: 
The input has three a and three b.

Input: S = “abababa” 
Output: Accepted 
Explanation: 
The input has three a and three b. 

To design a DFA we need to check the input character by character. These are a few steps that should be kept in mind while designing a DFA. 

• Think of all most of the possible input that can be accepted (like, in this example, aaabbb, bbbaaa, ababab, abaabb…etc).
• Create an initial transition state.
• Do transition on each input alphabet to other transition states.
• Reach a final state such that in each step the language used was accept(like, in this example, an equal number of a and b).

Designing steps:
Step 1: Create an initial state “A” which is indicated by —>. 
Step 2: Think of the possible string that can be aaabbb or bbbaaa which can occur by transition like,  

• The transition of input ‘a’ from state “A” to state “B”
• The transition of input ‘a’ from state “B” to state “C”
• The transition of input ‘a’ from state “C” to state “D”
• The transition of input ‘a’ from state “D” to dead state “Q2”
• The transition of input ‘b’ from state “D” to state “E”
• The transition of input ‘b’ from state “E” to state “F”
• The transition of input ‘b’ from state “F” to state “G”
• The transition of input ‘b’ from state “G” to dead state “Q2”

Step 3: Now work on a possibility like b’s comes after two a’s for example aababb, aabbab. 

• The transition of ‘b’ from state “C” to state “J”
• The transition of ‘a’ from state “J” to state “E”
• The transition of ‘b’ from state “J” to state “M”
• The transition of ‘a’ from state “M” to state “F”
• The transition of ‘b’ from state “M” to state “P”

The transition is shown in the diagram. 

Step-4: Now thinking of the possibility that starts with ‘aba’ and then fulfills the condition of the given language. For this following transitions to be done: 

• The transition of ‘b’ from state “B” to state “I”
• The transition of ‘a’ from state “I” to state “J”

Step-5: Now thinking of the possibility that starts with ‘abb’ and then fulfills the condition of the given language. For this following transitions to be done:

• The transition of ‘b’ from state “I” to state “L”
• The transition of ‘a’ from state “L” to state “M”

Step-6: Now there is a possibility that after reading one ‘a’ it reads all 3 b’s and then end execution by reading the remaining 2 a’s. For the transition of ‘b’ from state “L” to “O”. 

Step-7: there is a possibility that it reads ‘a’ after reading one ‘b’ and then it reads any combination of ‘a’ and ‘b’ so that string contains 3 a’s and 3 b’s.For this transition of ‘a’ is done from state”H” to state “I”. 

Step-8: Now, think about the strings starts with two b’s and the go for any combination of string to get the desired result for this we do a transition of ‘a’ from stare “K” to state “L”. 

Step-9: Now input alphabet ‘a’ of states D, E, F, G, and ‘b’ of states G, N, O, P are left for transitions.AS we have done all possibilities of the above language so the remaining transition will go to dead states “Q1″ and Q2”. 

• The transition of input ‘a’ from state “D” to dead state “Q1”
• The transition of input ‘a’ from state “E” to dead state “Q1”
• The transition of input ‘a’ from state “F” to dead state “Q1”
• The transition of input ‘a’ from state “G” to dead state “Q1”
• The transition of input ‘b’ from state “G” to dead state “Q2”
• The transition of input ‘b’ from state “N” to dead state “Q2”
• The transition of input ‘b’ from state “O” to dead state “Q2”
• The transition of input ‘b’ from state “P” to dead state “Q2”

Transition table of above DFA

STATES	INPUT (a)	INPUT (b)
—> A (initial state)	B	H
B	C	I
C	D	J
D	Q2 (dead state)	E
E	Q2 (dead state)	F
F	Q2 (dead state)	G*(final state)
G* (final state)	Q2 (dead state)	Q1 (dead state)
H	I	K
I	J	L
J	E	M
K	L	N
L	M	O
M	F	P
N	O	Q1 (dead state)
O	P	Q1 (dead state)
P	G* (final state)	Q1 (dead state)

Below is the implementation of the DFA:

C++

// C++ implementation of the
// DFA of permutation of three
// a's and three b's

#include<bits/stdc++.h>
using namespace std;

// declaration of state functions
void stateA(string),stateB(string),stateC(string),stateD(string);
void stateE(string),stateF(string),stateG(string),stateH(string);
void stateI(string),stateJ(string),stateK(string),stateL(string);
void stateM(string),stateN(string),stateO(string),stateP(string);
void stateQ1(string),stateQ2(string);

// State A
 void stateA(string n)
{
  if (n[0] == 'a')
    stateB(n.substr(1));
  else if (n[0] == 'b')
  {
    stateH(n.substr(1));
  }
 }

// State B
 void stateB(string n)
{
  if (n.length() == 0)
    cout << "string Not Accepted";
  else
  {
    if (n[0] == 'a')
      stateC(n.substr(1));
    else if (n[0] == 'b')
      stateI(n.substr(1));
  }
}

// State C
 void stateC(string n)
{
  if (n.length() == 0)
    cout << "string Not Accepted";
  else
  {
    if (n[0] == 'a')
      stateD(n.substr(1));
    else if (n[0] == 'b')
      stateJ(n.substr(1));
  }
}

// State D
 void stateD(string n)
{
  if (n.length() == 0)
    cout << "string Not Accepted";
  else
  {
    if (n[0] == 'a')
      stateQ2(n);
    else if (n[0] == 'b')
      stateE(n.substr(1));
  }
}

// State E
 void stateE(string n)
{
  if (n.length() == 0)
    cout << "string Not Accepted";
  else
  {
    if (n[0] == 'a')
      stateQ2(n);
    else if (n[0] == 'b')
      stateF(n.substr(1));
  }
}

// State F
 void stateF(string n)
{
  if (n.length() == 0)
    cout << "string Not Accepted";
  else
  {
    if (n[0] == 'a')
      stateQ2(n.substr(1));
    else if (n[0] == 'b')
      stateG(n.substr(1));
  }
}

// State G
 void stateG(string n)
{
  if (n.length() == 0)
    cout << "string Accepted";
  else
  {
    if (n[0] == 'a')
      stateQ2(n);
    else if (n[0] == 'b')
      stateQ2(n);
  }
}

// State H
 void stateH(string n)
{
  if (n.length() == 0)
    cout << "string Not Accepted";
  else
  {
    if (n[0] == 'a')
      stateI(n.substr(1));
    else if (n[0] == 'b')
      stateK(n.substr(1));
  }
}

// State I
 void stateI(string n)
{
  if (n.length() == 0)
    cout << "string Not Accepted";
  else
  {
    if (n[0] == 'a')
      stateJ(n.substr(1));
    else if (n[0] == 'b')
      stateL(n.substr(1));
  }
}

// State J
 void stateJ(string n)
{
  if (n.length() == 0)
    cout << "string Not Accepted";
  else
  {
    if (n[0] == 'a')
      stateE(n.substr(1));
    else if (n[0] == 'b')
      stateM(n.substr(1));
  }
}

// State K
 void stateK(string n)
{
  if (n.length() == 0)
    cout << "string Not Accepted";
  else
  {
    if (n[0] == 'a')
      stateL(n.substr(1));
    else if (n[0] == 'b')
      stateN(n.substr(1));
  }
}

// State L
 void stateL(string n)
{
  if (n.length() == 0)
    cout << "string Not Accepted";
  else
  {
    if (n[0] == 'a')
      stateM(n.substr(1));
    else if (n[0] == 'b')
      stateO(n.substr(1));
  }
}

// State M
 void stateM(string n)
{
  if (n.length() == 0)
    cout << "string Not Accepted";
  else
  {
    if (n[0] == 'a')
      stateF(n.substr(1));
    else if (n[0] == 'b')
      stateP(n.substr(1));
  }
}

// State N
 void stateN(string n)
{
  if (n.length() == 0)
    cout << "string Not Accepted";
  else
    if (n[0] =='a')
      stateO(n.substr(1));
  else if (n[0] == 'b')
    stateQ1(n);
}

// State Q
 void stateO(string n)
{
  if (n.length() == 0)
    cout << "string Not Accepted";
  else
  {
    if (n[0] == 'a')
      stateP(n.substr(1));
    else if (n[0] == 'b')
      stateQ1(n);
  }
}

// State P
 void stateP(string n)
{
  if (n.length() == 0)
    cout << "string Not Accepted";
  else
  {
    if (n[0] == 'a')
      stateG(n.substr(1));
    else if (n[0] == 'b')
      stateQ1(n.substr(1));
  }
}

// State Q1
 void stateQ1(string n)
{
  cout << "string Not Accepted";
}

// State Q2
 void stateQ2(string n)
{
  cout << "string Not Accepted";
}


int main()
{
  string n = "abaabb";

  // call stateA
  // to  check the input
  stateA(n);
}

Java

// Java implementation of the
// DFA of permutation of three
// a's and three b's
import java.util.*;

class GFG{

// State A
static void stateA(String n)
{
  if (n.charAt(0) == 'a')
    stateB(n.substring(1));
  else if (n.charAt(0) == 'b')
  {
    stateH(n.substring(1));
  }
 }

// State B
static void stateB(String n)
{
  if (n.length() == 0)
    System.out.print("String Not Accepted");
  else
  {
    if (n.charAt(0) == 'a')
      stateC(n.substring(1));
    else if (n.charAt(0) == 'b')
      stateI(n.substring(1));
  }
}

// State C
static void stateC(String n)
{
  if (n.length() == 0)
    System.out.print("String Not Accepted");
  else
  {
    if (n.charAt(0) == 'a')
      stateD(n.substring(1));
    else if (n.charAt(0) == 'b')
      stateJ(n.substring(1));
  }
}

// State D
static void stateD(String n)
{
  if (n.length() == 0)
    System.out.print("String Not Accepted");
  else
  {
    if (n.charAt(0) == 'a')
      stateQ2(n);
    else if (n.charAt(0) == 'b')
      stateE(n.substring(1));
  }
}

// State E
static void stateE(String n)
{
  if (n.length() == 0)
    System.out.print("String Not Accepted");
  else
  {
    if (n.charAt(0) == 'a')
      stateQ2(n);
    else if (n.charAt(0) == 'b')
      stateF(n.substring(1));
  }
}

// State F
static void stateF(String n)
{
  if (n.length() == 0)
    System.out.print("String Not Accepted");
  else
  {
    if (n.charAt(0) == 'a')
      stateQ2(n.substring(1));
    else if (n.charAt(0) == 'b')
      stateG(n.substring(1));
  }
}

// State G
static void stateG(String n)
{
  if (n.length() == 0)
    System.out.print("String Accepted");
  else
  {
    if (n.charAt(0) == 'a')
      stateQ2(n);
    else if (n.charAt(0) == 'b')
      stateQ2(n);
  }
}

// State H
static void stateH(String n)
{
  if (n.length() == 0)
    System.out.print("String Not Accepted");
  else
  {
    if (n.charAt(0) == 'a')
      stateI(n.substring(1));
    else if (n.charAt(0) == 'b')
      stateK(n.substring(1));
  }
}

// State I
static void stateI(String n)
{
  if (n.length() == 0)
    System.out.print("String Not Accepted");
  else
  {
    if (n.charAt(0) == 'a')
      stateJ(n.substring(1));
    else if (n.charAt(0) == 'b')
      stateL(n.substring(1));
  }
}

// State J
static void stateJ(String n)
{
  if (n.length() == 0)
    System.out.print("String Not Accepted");
  else
  {
    if (n.charAt(0) == 'a')
      stateE(n.substring(1));
    else if (n.charAt(0) == 'b')
      stateM(n.substring(1));
  }
}

// State K
static void stateK(String n)
{
  if (n.length() == 0)
    System.out.print("String Not Accepted");
  else
  {
    if (n.charAt(0) == 'a')
      stateL(n.substring(1));
    else if (n.charAt(0) == 'b')
      stateN(n.substring(1));
  }
}

// State L
static void stateL(String n)
{
  if (n.length() == 0)
    System.out.print("String Not Accepted");
  else
  {
    if (n.charAt(0) == 'a')
      stateM(n.substring(1));
    else if (n.charAt(0) == 'b')
      stateO(n.substring(1));
  }
}

// State M
static void stateM(String n)
{
  if (n.length() == 0)
    System.out.print("String Not Accepted");
  else
  {
    if (n.charAt(0) == 'a')
      stateF(n.substring(1));
    else if (n.charAt(0) == 'b')
      stateP(n.substring(1));
  }
}

// State N
static void stateN(String n)
{
  if (n.length() == 0)
    System.out.print("String Not Accepted");
  else
    if (n.charAt(0) =='a')
      stateO(n.substring(1));
  else if (n.charAt(0) == 'b')
    stateQ1(n);
}

// State Q
static void stateO(String n)
{
  if (n.length() == 0)
    System.out.print("String Not Accepted");
  else
  {
    if (n.charAt(0) == 'a')
      stateP(n.substring(1));
    else if (n.charAt(0) == 'b')
      stateQ1(n);
  }
}

// State P
static void stateP(String n)
{
  if (n.length() == 0)
    System.out.print("String Not Accepted");
  else
  {
    if (n.charAt(0) == 'a')
      stateG(n.substring(1));
    else if (n.charAt(0) == 'b')
      stateQ1(n.substring(1));
  }
}

// State Q1
static void stateQ1(String n)
{
  System.out.print("String Not Accepted");
}

// State Q2
static void stateQ2(String n)
{
  System.out.print("String Not Accepted");
}

// Driver code
public static void main(String[] args)
{

  // Take String input
  String n = "abaabb";

  // Call stateA
  // to check the input
  stateA(n);
}
}

// This code is contributed by pratham76

Python3

# Python3 implementation of the
# DFA of permutation of three
# a's and three b's

# State A
def stateA(n):
    if(n[0]=='a'):
        stateB(n[1:])
    elif (n[0]=='b'):
        stateH(n[1:])

# State B
def stateB(n):
    if(len(n)== 0):
        print("String Not Accepted")
    else:
        if(n[0]=='a'):
            stateC(n[1:])
        elif (n[0]=='b'):
            stateI(n[1:])

# State C
def stateC(n):
    if(len(n)== 0):
        print("String Not Accepted")
    else:
        if(n[0]=='a'):
            stateD(n[1:])
        elif (n[0]=='b'):
            stateJ(n[1:])

# State D
def stateD(n):
    if(len(n)== 0):
        print("String Not Accepted")
    else:
        if(n[0]=='a'):
            stateQ2(n)
        elif (n[0]=='b'):
            stateE(n[1:])

# State E
def stateE(n):
    if(len(n)== 0):
        print("String Not Accepted")
    else:
        if(n[0]=='a'):
            stateQ2(n)
        elif (n[0]=='b'):
            stateF(n[1:])

# State F
def stateF(n):
    if(len(n)== 0):
        print("String Not Accepted")
    else:
        if(n[0]=='a'):
            stateQ2(n[1:])
        elif (n[0]=='b'):
            stateG(n[1:])

# State G
def stateG(n):
    if(len(n)== 0):
        print("String Accepted")
    else:
        if(n[0]=='a'):
            stateQ2(n)
        elif (n[0]=='b'):
            stateQ2(n)

# State H
def stateH(n):
    if(len(n)== 0):
        print("String Not Accepted")
    else:
        if(n[0]=='a'):
            stateI(n[1:])
        elif (n[0]=='b'):
            stateK(n[1:])

# State I
def stateI(n):
    if(len(n)== 0):
        print("String Not Accepted")
    else:
        if(n[0]=='a'):
            stateJ(n[1:])
        elif (n[0]=='b'):
            stateL(n[1:])

# State J
def stateJ(n):
    if(len(n)== 0):
        print("String Not Accepted")
    else:
        if(n[0]=='a'):
            stateE(n[1:])
        elif (n[0]=='b'):
            stateM(n[1:])

# State K
def stateK(n):
    if(len(n)== 0):
        print("String Not Accepted")
    else:
        if(n[0]=='a'):
            stateL(n[1:])
        elif (n[0]=='b'):
            stateN(n[1:])

# State L
def stateL(n):
    if(len(n)== 0):
        print("String Not Accepted")
    else:
        if(n[0]=='a'):
            stateM(n[1:])
        elif (n[0]=='b'):
            stateO(n[1:])

# State M
def stateM(n):
    if(len(n)== 0):
        print("String Not Accepted")
    else:
        if(n[0]=='a'):
            stateF(n[1:])
        elif (n[0]=='b'):
            stateP(n[1:])

# State N
def stateN(n):
    if(len(n)== 0):
        print("String Not Accepted")
    else:
        if(n[0]=='a'):
            stateO(n[1:])
        elif (n[0]=='b'):
            stateQ1(n)

# State Q
def stateO(n):
    if(len(n)== 0):
        print("String Not Accepted")
    else:
        if(n[0]=='a'):
            stateP(n[1:])
        elif (n[0]=='b'):
            stateQ1(n)

# State P
def stateP(n):
    if(len(n)== 0):
        print("String Not Accepted")
    else:
        if(n[0]=='a'):
            stateG(n[1:])
        elif (n[0]=='b'):
            stateQ1(n[1:])

# State Q1
def stateQ1(n):
    print("String Not Accepted")

# State Q2
def stateQ2(n):
    print("String Not Accepted")

# take string input
n = "abaabb"

# call stateA
# to check the input
stateA(n)

C#

// C# implementation of the
// DFA of permutation of three
// a's and three b's
using System;
using System.Collections;
class GFG{

// State A
static void stateA(string n)
{
  if(n[0] == 'a')
    stateB(n.Substring(1));
  else if (n[0] == 'b')
  {
    stateH(n.Substring(1));
  }
 }

// State B
static void stateB(string n)
{
  if(n.Length == 0)
    Console.Write("String Not Accepted");
  else
  {
    if(n[0] == 'a')
      stateC(n.Substring(1));
    else if (n[0] == 'b')
      stateI(n.Substring(1));
  }
}

// State C
static void stateC(string n)
{
  if(n.Length == 0)
    Console.Write("String Not Accepted");
  else
  {
    if(n[0] == 'a')
      stateD(n.Substring(1));
    else if (n[0] == 'b')
      stateJ(n.Substring(1));
  }
}

// State D
static void stateD(string n)
{
  if(n.Length == 0)
    Console.Write("String Not Accepted");
  else
  {
    if(n[0] == 'a')
      stateQ2(n);
    else if (n[0] == 'b')
      stateE(n.Substring(1));
  }
}

// State E
static void stateE(string n)
{
  if(n.Length == 0)
    Console.Write("String Not Accepted");
  else
  {
    if(n[0] == 'a')
      stateQ2(n);
    else if (n[0] == 'b')
      stateF(n.Substring(1));
  }
}

// State F
static void stateF(string n)
{
  if(n.Length == 0)
    Console.Write("String Not Accepted");
  else
  {
    if(n[0] == 'a')
      stateQ2(n.Substring(1));
    else if (n[0] == 'b')
      stateG(n.Substring(1));
  }
}

// State G
static void stateG(string n)
{
  if(n.Length == 0)
    Console.Write("String Accepted");
  else
  {
    if(n[0] == 'a')
      stateQ2(n);
    else if (n[0] == 'b')
      stateQ2(n);
  }
}

// State H
static void stateH(string n)
{
  if(n.Length == 0)
    Console.Write("String Not Accepted");
  else
  {
    if(n[0] == 'a')
      stateI(n.Substring(1));
    else if (n[0] == 'b')
      stateK(n.Substring(1));
  }
}

// State I
static void stateI(string n)
{
  if(n.Length == 0)
    Console.Write("String Not Accepted");
  else
  {
    if(n[0] == 'a')
      stateJ(n.Substring(1));
    else if (n[0] == 'b')
      stateL(n.Substring(1));
  }
}

// State J
static void stateJ(string n)
{
  if(n.Length == 0)
    Console.Write("String Not Accepted");
  else
  {
    if(n[0] == 'a')
      stateE(n.Substring(1));
    else if (n[0] == 'b')
      stateM(n.Substring(1));
  }
}

// State K
static void stateK(string n)
{
  if(n.Length == 0)
    Console.Write("String Not Accepted");
  else
  {
    if(n[0] == 'a')
      stateL(n.Substring(1));
    else if (n[0] == 'b')
      stateN(n.Substring(1));
  }
}

// State L
static void stateL(string n)
{
  if(n.Length == 0)
    Console.Write("String Not Accepted");
  else
  {
    if(n[0] == 'a')
      stateM(n.Substring(1));
    else if (n[0] == 'b')
      stateO(n.Substring(1));
  }
}

// State M
static void stateM(string n)
{
  if(n.Length == 0)
    Console.Write("String Not Accepted");
  else{
    if(n[0] == 'a')
      stateF(n.Substring(1));
    else if (n[0] == 'b')
      stateP(n.Substring(1));
  }
}

// State N
static void stateN(string n)
{
  if(n.Length == 0)
    Console.Write("String Not Accepted");
  else
    if(n[0] =='a')
      stateO(n.Substring(1));
  else if (n[0] == 'b')
    stateQ1(n);
}

// State Q
static void stateO(string n)
{
  if(n.Length == 0)
    Console.Write("String Not Accepted");
  else
  {
    if(n[0] == 'a')
      stateP(n.Substring(1));
    else if(n[0] == 'b')
      stateQ1(n);
  }
}

// State P
static void stateP(string n)
{
  if(n.Length == 0)
    Console.Write("String Not Accepted");
  else
  {
    if(n[0] == 'a')
      stateG(n.Substring(1));
    else if (n[0] == 'b')
      stateQ1(n.Substring(1));
  }
}

// State Q1
static void stateQ1(string n)
{
  Console.Write("String Not Accepted");
}

// State Q2
static void stateQ2(string n)
{
  Console.Write("String Not Accepted");
}

// Driver code
public static void Main (string[] args)
{
  // Take string input
  string n = "abaabb";

  // Call stateA
  // to check the input
  stateA(n);
}
}

// This code is contributed by rutvik_56

Javascript

<script>

      // JavaScript implementation of the
      // DFA of permutation of three
      // a's and three b's
      // State A
      function stateA(n) {
        if (n[0] === "a") stateB(n.substring(1));
        else if (n[0] === "b") {
          stateH(n.substring(1));
        }
      }

      // State B
      function stateB(n) {
        if (n.length === 0)
        document.write("String Not Accepted");
        else {
          if (n[0] === "a") stateC(n.substring(1));
          else if (n[0] === "b") stateI(n.substring(1));
        }
      }

      // State C
      function stateC(n) {
        if (n.length === 0)
        document.write("String Not Accepted");
        else {
          if (n[0] === "a") stateD(n.substring(1));
          else if (n[0] === "b") stateJ(n.substring(1));
        }
      }

      // State D
      function stateD(n) {
        if (n.length === 0)
        document.write("String Not Accepted");
        else {
          if (n[0] === "a") stateQ2(n);
          else if (n[0] === "b") stateE(n.substring(1));
        }
      }

      // State E
      function stateE(n) {
        if (n.length === 0)
        document.write("String Not Accepted");
        else {
          if (n[0] === "a") stateQ2(n);
          else if (n[0] === "b") stateF(n.substring(1));
        }
      }

      // State F
      function stateF(n) {
        if (n.length === 0)
        document.write("String Not Accepted");
        else {
          if (n[0] === "a") stateQ2(nsubstring(1));
          else if (n[0] === "b") stateG(n.substring(1));
        }
      }

      // State G
      function stateG(n) {
        if (n.length === 0)
        document.write("String Accepted");
        else {
          if (n[0] === "a") stateQ2(n);
          else if (n[0] === "b") staseQ2(n);
        }
      }

      // State H
      function stateH(n) {
        if (n.length === 0)
        document.write("String Not Accepted");
        else {
          if (n[0] === "a") stateI(n.substring(1));
          else if (n[0] === "b") stateK(n.substring(1));
        }
      }

      // State I
      function stateI(n) {
        if (n.length === 0)
        document.write("String Not Accepted");
        else {
          if (n[0] === "a") stateJ(n.substring(1));
          else if (n[0] === "b") stateL(n.substring(1));
        }
      }

      // State J
      function stateJ(n) {
        if (n.length === 0)
        document.write("String Not Accepted");
        else {
          if (n[0] === "a") stateE(n.substring(1));
          else if (n[0] === "b") stateM(n.substring(1));
        }
      }

      // State K
      function stateK(n) {
        if (n.length === 0)
        document.write("String Not Accepted");
        else {
          if (n[0] === "a") stateL(n.substring(1));
          else if (n[0] === "b") stateN(n.substring(1));
        }
      }

      // State L
      function stateL(n) {
        if (n.length === 0)
        document.write("String Not Accepted");
        else {
          if (n[0] === "a") stateM(n.substring(1));
          else if (n[0] === "b") stateO(n.substring(1));
        }
      }

      // State M
      function stateM(n) {
        if (n.length === 0)
        document.write("String Not Accepted");
        else {
          if (n[0] === "a") stateF(n.substring(1));
          else if (s[0] === "b") stateP((n.Substr = ing(s)));
        }
      }

      // State N
      function stateN(n) {
        if (n.length === 0)
        document.write("String Not Accepted");
        else if (n[0] === "a") stateO(n.substring(1));
        else if (n[s] === "b") stateQ1(n);
      }

      // Stste Q
      function stateO(n) {
        if (n.length === 0)
        document.write("String Not Accepted");
        else {
          if (n[0] === "a") stateP(n.substring(1));
          else if (n[0] === "b") staseQ1(n);
        }
      }

      // State P
      function stateP(n) {
        if (n.length === 0)
        document.write("String Not Accepted");
        else {
          if (n[0] === "a") stateG(n.substring(1));
          else if (n[0] === "b") stateQ1(nsSubstring(1));
        }
      }

      // State Q1
      function stateQ1(n) {
        document.write("String Not Accepted");
      }

      // State Q2
      function stateQ2(n) {
        document.write("String Not Accepted");
      }

      // Driver code
      // Take string input
      var n = "abaabb";

      // Call stateA
      // to check the input
      stateA(n);

</script>

Output:

String Accepted

Time Complexity: O(N)  
Auxiliary Space: O(N)