Implementing DFA for no runs of length less than 4 for input (a,b)

Last Updated : 08 Mar, 2023

DFA or Deterministic Finite Automata is a finite state machine, in which on every input alphabet a transition is done from one state to another state according to set of defined rules as per the need of string acceptance.
In this particular problem, runs of length is the factor to think about.The input alphabets are {a, b}. No runs of length less than 4 means any input alphabets repeats itself minimum 4 times.

Example:

Input: n = “aaabab”
Output: string not accepted
Explanation: The starting letter a is not repeated at least 4 times. Hence DFA failed.

Input: n = “aaaabbbbaaaabbbbbaaaaa”
Output: string accepted
Explanation: Every unique occurrence of a and b are repeated at least 4 times. Hence DFA passed.

Designing DFA step by step:
Step-1: First we have to think about what input alphabet is inputted. As this is about minimum 4 runs of length. Take input alphabet is ‘a’ on state “A” and mark this state as initial state. The following transition occur on input ‘a’:

From state “A” to state “B”
From state “B” to state “C”
From state “C” to state “D”
From state “D” to state “E”

input of run of length 4

Step-2: As in above step, minimum 4 a’s are inputted which is acceptable so make state “E” is final state. Also runs of length more than 4 is acceptable so put self loop of ‘a’ on final state “E”.

marks state “E” to final state

Step-3: Till now machine design is done with input alphabet ‘a’.But input alphabet ‘b’ of state “A” is left to deal with. Now do the same process with input alphabet ‘b’ on state “A”.The following transition occur on input ‘b’:

From state “A” to state “F”
From state “F” to state “G”
From state “G” to state “H”
From state “H” to state “Q”

Mark state “Q” to final state. And also runs of length more than 4 is also acceptable so put self loop on final state “Q”.

input alphabet ‘b’ transitions

Step-4: Till now we have done with only single input a or b, i.e, aaaa, and bbbb, but now deal with both input such as aaaabbbb or aaaabbbbaaaaa etc.
For this transition of input ‘b’ from state “E” to state “F” and transition of input ‘a’ from state “Q” to state “B”.

Step-5: Now dealing with remaining input alphabets, till now designed machine have covered all possible acceptable cases and nor remaining input alphabets will go to dead state”DS”.

final design

Transition Table of above DFA:
Here “A” is initial state and “E” and “Q” are final states. DS is termed as DEAD STATE

Transition Table

Python implementation of above DFA:

C++

#include <iostream>
#include <string>
 
// Class to check the states of the StateMachine
class StateMachine {
public:
    // function to check the stateA
    static void checkStateA(std::string n)
    {
        // if length of is 0
        // print string not accepted
        if (n.length() == 0) {
            std::cout << "String not accepted" << std::endl;
        }
        else {
            // if 'a' is found
            // call stateB function
            // else call stateF
            // function
            if (n.at(0) == 'a') {
                stateB(n.substr(1));
            }
            else {
                stateF(n.substr(1));
            }
        }
    }
 
    // function to check the stateB
    static void stateB(std::string n)
    {
        // if length of is 0
        // print string not accepted
        if (n.length() == 0) {
            std::cout << "String not accepted" << std::endl;
        }
        else {
            // if 'a' is found
            // call stateC function
            // print string not
            // accepted
            if (n.at(0) == 'a') {
                stateC(n.substr(1));
            }
            else {
                std::cout << "String not accepted"
                          << std::endl;
            }
        }
    }
 
    // function to check the stateC
    static void stateC(std::string n)
    {
        // if length of is 0
        // print string not accepted
        if (n.length() == 0) {
            std::cout << "String not accepted" << std::endl;
        }
        else {
            // if 'a' is found
            // call stateD function
            // print string not
            // accepted
            if (n.at(0) == 'a') {
                stateD(n.substr(1));
            }
            else {
                std::cout << "String not accepted"
                          << std::endl;
            }
        }
    }
 
    // function to check the stateD
    static void stateD(std::string n)
    {
        // if length of is 0
        // print string not accepted
        if (n.length() == 0) {
            std::cout << "String not accepted" << std::endl;
        }
        else {
            // if 'a' is found
            // call stateE function
            // print string not
            // accepted
            if (n.at(0) == 'a') {
                stateE(n.substr(1));
            }
            else {
                std::cout << "String not accepted"
                          << std::endl;
            }
        }
    }
 
    // function to check the stateE
    static void stateE(std::string n)
    {
        // if length of is 0
        // print string accepted
        if (n.length() == 0) {
            std::cout << "String accepted" << std::endl;
        }
        // if 'a' is found
        // call stateE function
        // if 'b' is found
        // call stateF function
        else if (n.at(0) == 'a') {
            stateE(n.substr(1));
        }
        else if (n.at(0) == 'b') {
            stateF(n.substr(1));
        }
    }
 
    // function to check the stateF
    static void stateF(std::string n)
    {
        // if length of is 0
        // print string not accepted
        if (n.length() == 0) {
            std::cout << "String not accepted" << std::endl;
        }
        else {
            // if 'b' is found
            // call stateG function
            // print string not
            // accepted
            if (n.at(0) == 'b') {
                stateG(n.substr(1));
            }
            else {
                std::cout << "String not accepted"
                          << std::endl;
            }
        }
    }
 
    // function to check the stateG
    static void stateG(std::string n)
    {
        // if length of is 0
        // print string not accepted
        if (n.length() == 0) {
            std::cout << "String not accepted" << std::endl;
        }
        else {
            // if 'b' is found
            // call stateHfunction
            // print string not
            // accepted
            if (n.at(0) == 'b') {
                stateH(n.substr(1));
            }
            else {
                std::cout << "String not accepted"
                          << std::endl;
            }
        }
    }
 
    // function to check the stateH
    static void stateH(std::string n)
    {
        // if length of is 0
        // print string not accepted
        if (n.length() == 0) {
            std::cout << "String not accepted" << std::endl;
        }
        else {
            // if 'b' is found
            // call stateQ function
            // print string not
            // accepted
            if (n.at(0) == 'b') {
                stateQ(n.substr(1));
            }
            else {
                std::cout << "String not accepted"
                          << std::endl;
            }
        }
    }
 
    // function to check the stateQ
    static void stateQ(std::string n)
    {
        // if length of is 0
        // print string accepted
        if (n.length() == 0) {
            std::cout << "String accepted" << std::endl;
        }
        else {
            // if 'b' is found
            // call stateQ function
            // else call stateB function
            if (n.at(0) == 'b') {
                stateQ(n.substr(1));
            }
            else if (n.at(0) == 'a') {
                stateB(n.substr(1));
            }
        }
    }
};
 
// Driver code
int main()
{
    // input string 1
    std::string n = "aaaabbbbbaaaa";
 
    // function call to check the string
    StateMachine::checkStateA(n);
 
    // input string 2
    n = "aaaabbb";
 
    // function call to check the string
    StateMachine::checkStateA(n);
    return 0;
}

Java

public class StateMachine {
 
    // function to check the stateA
    public static void checkStateA(String n) {
       
        // if length of is 0
        // print string not accepted
        if(n.length() == 0) {
            System.out.println("String not accepted");
        }
        else {
            // if 'a' is found 
            // call stateB function
            // else call stateF
            // function
            if(n.charAt(0) == 'a') {
                stateB(n.substring(1));
            }
            else {
                stateF(n.substring(1));
            }
        }
    }
 
    // function to check the stateB
    public static void stateB(String n) {
       
        // if length of is 0
        // print string not accepted
        if(n.length() == 0) {
            System.out.println("String not accepted");
        }
        else {
           
            // if 'a' is found 
            // call stateC function
            // print string not
            // accepted
            if(n.charAt(0) == 'a') {
                stateC(n.substring(1));
            }
            else {
                System.out.println("String not accepted");
            }
        }
    }
 
    // function to check the stateC
    public static void stateC(String n) {
       
        // if length of is 0
        // print string not accepted
        if(n.length() == 0) {
            System.out.println("String not accepted");
        }
        else {
           
            // if 'a' is found 
            // call stateD function
            // print string not
            // accepted
            if(n.charAt(0) == 'a') {
                stateD(n.substring(1));
            }
            else {
                System.out.println("String not accepted");
            }
        }
    }
 
    // function to check the stateD
    public static void stateD(String n) {
       
        // if length of is 0
        // print string not accepted
        if(n.length() == 0) {
            System.out.println("String not accepted");
        }
        else {
           
            // if 'a' is found 
            // call stateE function
            // print string not
            // accepted
            if(n.charAt(0) == 'a') {
                stateE(n.substring(1));
            }
            else {
                System.out.println("String not accepted");
            }
        }
    }
 
    // function to check the stateE
    public static void stateE(String n) {
       
        // if length of is 0
        // print string accepted
        if(n.length() == 0) {
            System.out.println("String accepted");
        }
       
        // if 'a' is found 
        // call stateE function
        // if 'b' is found 
        // call stateF function    
        else if(n.charAt(0) == 'a') {
            stateE(n.substring(1));
        }
        else if(n.charAt(0) == 'b') {
            stateF(n.substring(1));
        }
    }
 
    // function to check the stateF
    public static void stateF(String n) {
       
        // if length of is 0
        // print string not accepted
        if(n.length() == 0) {
            System.out.println("String not accepted");
        }
        else {
           
            // if 'b' is found 
            // call stateG function
            // print string not
            // accepted
            if(n.charAt(0) == 'b') {
                stateG(n.substring(1));
            }
            else {
                System.out.println("String not accepted");
            }
        }
    }
 
    // function to check the stateG
    public static void stateG(String n) {
       
        // if length of is 0
        // print string not accepted
        if(n.length() == 0) {
            System.out.println("String not accepted");
        }
        else {
           
            // if 'b' is found 
            // call stateHfunction
            // print string not
            // accepted
            if(n.charAt(0) == 'b') {
                stateH(n.substring(1));
            }
            else {
                System.out.println("String not accepted");
            }
        }
    }
 
    // function to check the stateH
    public static void stateH(String n) {
       
        // if length of is 0
        // print string not accepted
        if(n.length() == 0) {
            System.out.println("String not accepted");
        }
        else {
           
            // if 'b' is found 
            // call stateQ function
            // print string not
            // accepted
            if(n.charAt(0) == 'b') {
                stateQ(n.substring(1));
            }
            else {
                System.out.println("String not accepted");
            }
        }
    }
 
    // function to check the stateQ
    public static void stateQ(String n) {
       
        // if length of is 0
        // print string accepted
        if(n.length() == 0) {
            System.out.println("String accepted");
        }
        else {
           
            // if 'b' is found 
            // call stateQ function
            // else call stateB function
            if(n.charAt(0) == 'b') {
                stateQ(n.substring(1));
            }
            else if(n.charAt(0) == 'a') {
                stateB(n.substring(1));
            }
        }
    }
 
    // Driver code
    public static void main(String[] args) {
       
        // input string 1
        String n = "aaaabbbbbaaaa";
 
        // function call to check the string
        checkStateA(n);
 
        // input string 2
        n = "aaaabbb";
 
        // function call to check the string
        checkStateA(n);
    }
}

Python3

def checkStateA(n):
    # if length of is 0
    # print string not accepted
    if(len(n)== 0):
        print("string not accepted")
         
    else:
        # if 'a' is found 
        # call stateB function
        # else call stateF
        # function
        if(n[0]=='a'):
            stateB(n[1:])
        else:
            stateF(n[1:])
     
 
def stateB(n):
    # if length of is 0
    # print string not accepted
    if (len(n)== 0):
        print("string not accepted")
         
    else:    
        # if 'a' is found 
        # call stateC function
        # print string not
        # accepted
        if(n[0]=='a'):
            stateC(n[1:])
        else:
            print("string not accepted")
     
     
def stateC(n):
    # if length of is 0
    # print string not accepted
    if (len(n)== 0):
        print("string not accepted")
         
    else:   
        # if 'a' is found 
        # call stateD function
        # print string not
        # accepted
        if(n[0]=='a'):
            stateD(n[1:])
        else:
            print("string not accepted")
     
     
def stateD(n):
    # if length of is 0
    # print string not accepted
    if(len(n)== 0):
        print("string not accepted")
         
    else:    
        # if 'a' is found 
        # call stateE function
        # print string not
        # accepted
        if(n[0]=='a'):
            stateE(n[1:])
        else:
            print("string not accepted")
         
         
def stateE(n):
    # if length of is 0
    # print string accepted
    if(len(n)== 0):
        print("string accepted")
         
    # if 'a' is found 
    # call stateE function
    # if 'b' is found 
    # call stateF function    
    elif(n[0]=='a'):
        stateE(n[1:])
    elif(n[0]=='b'):
        stateF(n[1:])
         
         
def stateF(n):
    # if length of is 0
    # print string not accepted
    if(len(n)== 0):
        print("string not accepted")
         
    else: 
        # if 'b' is found 
        # call stateG function
        # print string not
        # accepted
        if(n[0]=='b'):
            stateG(n[1:])
        else:
            print("string not accepted")
     
     
def stateG(n):
    # if length of is 0
    # print string not accepted
    if(len(n)== 0):
        print("string not accepted")
         
    else:    
        # if 'b' is found 
        # call stateHfunction
        # print string not
        # accepted
        if(n[0]=='b'):
            stateH(n[1:])
        else:
            print("string not accepted")
             
             
def stateH(n):
    # if length of is 0
    # print string not accepted
    if(len(n)== 0):
        print("string not accepted")
         
    else:  
        # if 'b' is found 
        # call stateQ function
        # print string not
        # accepted
        if(n[0]=='b'):
            stateQ(n[1:])
        else:
            print("string not accepted")  
             
             
def stateQ(n):
    # if length of is 0
    # print string accepted
    if(len(n)== 0):
        print("string accepted")
         
    else:   
        # if 'b' is found 
        # call stateQ function
        # else call stateB function
        if(n[0]=='b'):
            stateQ(n[1:])
        elif(n[0]=='a'):
            stateB(n[1:])            
     
         
         
 
# Driver code
if __name__ == '__main__':
 
    # input string 1
    n ="aaaabbbbbaaaa"
 
    # function call to check the string
    checkStateA(n)
 
    # input string 2
    n ="aaaabbb"
 
    # function call to check the string
    checkStateA(n)

C#

using System;
 
// Class to check the states of the StateMachine
public class StateMachine {
 
  // function to check the stateA
  public static void CheckStateA(string n)
  {
 
    // if length of is 0
    // print string not accepted
    if (n.Length == 0)
      Console.WriteLine("String not accepted");
    else
    {
 
      // if 'a' is found
      // call stateB function
      // else call stateF
      // function
      if (n[0] == 'a')
        StateB(n.Substring(1));
      else
        StateF(n.Substring(1));
    }
  }
 
  // function to check the stateB
  public static void StateB(string n)
  {
 
    // if length of is 0
    // print string not accepted
    if (n.Length == 0)
      Console.WriteLine("String not accepted");
    else {
      // if 'a' is found
      // call stateC function
      // print string not
      // accepted
      if (n[0] == 'a')
        StateC(n.Substring(1));
      else
        Console.WriteLine("String not accepted");
    }
  }
  // function to check the stateC
  public static void StateC(string n)
  {
 
    // if length of is 0
    // print string not accepted
    if (n.Length == 0)
      Console.WriteLine("String not accepted");
    else {
      // if 'a' is found
      // call stateD function
      // print string not
      // accepted
      if (n[0] == 'a')
        StateD(n.Substring(1));
      else
        Console.WriteLine("String not accepted");
    }
  }
 
  // function to check the stateD
  public static void StateD(string n)
  {
 
    // if length of is 0
    // print string not accepted
    if (n.Length == 0)
      Console.WriteLine("String not accepted");
    else {
      // if 'a' is found
      // call stateE function
      // print string not
      // accepted
      if (n[0] == 'a')
        StateE(n.Substring(1));
      else
        Console.WriteLine("String not accepted");
    }
  }
  // function to check the stateE
  public static void StateE(string n)
  {
    // if length of is 0
    // print string accepted
    if (n.Length == 0)
      Console.WriteLine("String accepted");
    // if 'a' is found
    // call stateE function
    // if 'b' is found
    // call stateF function
    else if (n[0] == 'a')
      StateE(n.Substring(1));
    else if (n[0] == 'b')
      StateF(n.Substring(1));
  }
 
  // function to check the stateF
  public static void StateF(string n)
  {
 
    // if length of is 0
    // print string not accepted
    if (n.Length == 0)
      Console.WriteLine("String not accepted");
    else {
      // if 'b' is found
      // call stateG function
      // print string not
      // accepted
      if (n[0] == 'b')
        StateG(n.Substring(1));
      else
        Console.WriteLine("String not accepted");
    }
  }
 
  // function to check the stateG
  public static void StateG(string n)
  {
 
    // if length of is 0
    // print string not accepted
    if (n.Length == 0)
      Console.WriteLine("String not accepted");
    else {
      // if 'b' is found
      // call stateHfunction
      // print string not
      // accepted
      if (n[0] == 'b')
        StateH(n.Substring(1));
      else
        Console.WriteLine("String not accepted");
    }
  }
 
  // function to check the stateH
  public static void StateH(string n)
  {
 
    // if length of is 0
    // print string not accepted
    if (n.Length == 0)
      Console.WriteLine("String not accepted");
    else {
      // if 'b' is found
      // call stateQ function
      // print string not
      // accepted
      if (n[0] == 'b')
        StateQ(n.Substring(1));
      else
        Console.WriteLine("String not accepted");
    }
  }
 
  // function to check the stateQ
  public static void StateQ(string n)
  {
 
    // if length of is 0
    // print string accepted
    if (n.Length == 0)
      Console.WriteLine("String accepted");
    else {
 
      // if 'b' is found
      // call stateQ function
      // else call stateB function
      if (n[0] == 'b')
        StateQ(n.Substring(1));
      else if (n[0] == 'a')
        StateB(n.Substring(1));
    }
  }
}
 
public class Program {
  public static void Main(string[] args)
  {
    // input string 1
    string n = "aaaabbbbbaaaa";
 
    // function call to check the string
    StateMachine.CheckStateA(n);
 
    // input string 2
    n = "aaaabbb";
 
    // function call to check the string
    StateMachine.CheckStateA(n);
  }
}

Javascript

function checkStateA(n) {
  if (n.length === 0) {
    console.log("string not accepted");
  } else {
    if (n[0] === 'a') {
      stateB(n.substring(1));
    } else {
      stateF(n.substring(1));
    }
  }
}
 
function stateB(n) {
  if (n.length === 0) {
    console.log("string not accepted");
  } else {
    if (n[0] === 'a') {
      stateC(n.substring(1));
    } else {
      console.log("string not accepted");
    }
  }
}
 
function stateC(n) {
  if (n.length === 0) {
    console.log("string not accepted");
  } else {
    if (n[0] === 'a') {
      stateD(n.substring(1));
    } else {
      console.log("string not accepted");
    }
  }
}
 
function stateD(n) {
  if (n.length === 0) {
    console.log("string not accepted");
  } else {
    if (n[0] === 'a') {
      stateE(n.substring(1));
    } else {
      console.log("string not accepted");
    }
  }
}
 
function stateE(n) {
  if (n.length === 0) {
    console.log("string accepted");
  } else if (n[0] === 'a') {
    stateE(n.substring(1));
  } else if (n[0] === 'b') {
    stateF(n.substring(1));
  }
}
 
function stateF(n) {
  if (n.length === 0) {
    console.log("string not accepted");
  } else {
    if (n[0] === 'b') {
      stateG(n.substring(1));
    } else {
      console.log("string not accepted");
    }
  }
}
 
function stateG(n) {
  if (n.length === 0) {
    console.log("string not accepted");
  } else {
    if (n[0] === 'b') {
      stateH(n.substring(1));
    } else {
      console.log("string not accepted");
    }
  }
}
 
function stateH(n) {
  if (n.length === 0) {
    console.log("string not accepted");
  } else {
    if (n[0] === 'b') {
      stateQ(n.substring(1));
    } else {
      console.log("string not accepted");
    }
  }
}
 
function stateQ(n) {
  if (n.length === 0) {
    console.log("string accepted");
  } else if (n[0] === 'b') {
    stateQ(n.substring(1));
  } else if (n[0] === 'a') {
    stateB(n.substring(1));
  }
}
 
// Driver code
let n = "aaaabbbbbaaaa";
checkStateA(n);
n = "aaaabbb";
checkStateA(n);