Program to construct a DFA which accepts the language L = {a^N | N ≥ 1}

Last Updated : 28 Jun, 2021

Given a string S of size N, the task is to design a Deterministic Finite Automata (DFA) for accepting the language L = {a^N | N ? 1}. The regular language L is {a, aa, aaa, aaaaaaa…, }. If the given string follows the given language L, then print “Accepted”. Otherwise, print “Not Accepted”.

Examples:

Input: S = “aaabbb”
Output: Not Accepted
Explanation: String must only contain a.

Input: S = “aa”
Output: Accepted

Approach: The idea by which the automata lead to acceptance of string is stated below in steps:

The automata will accept all the strings containing only the character ‘a’. If the user tried to input any character other than ‘a’, the machine will reject it.
Let the state q0 is the initial state represent the set of all strings of length 0, state q1 is the final state represent the set of all strings from 1 to N.
State q1 contains a self-loop of a which indicates that it can be repeated as required.
The logic for code is very basic as it has only a for loop which counts the number of a’s in a given string, if the count of a is the same as N then it will be accepted. Otherwise, the string will be rejected.

DFA State Transition Diagram:

Below is the implementation of the above approach:

C++

// C++ program for the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to check whether the string
// S satisfy the given DFA or not
void isAcceptedDFA(string s, int N)
{
    // Stores the count of characters
    int count = 0;
 
    // Iterate over the range [0, N]
    for (int i = 0; i < N; i++) {
 
        // Count and check every
        // element for 'a'
        if (s[i] == 'a')
            count++;
    }
 
    // If string matches with DFA
    if (count == N && count != 0) {
        cout << "Accepted";
    }
 
    // If not matches
    else {
        cout << "Not Accepted";
    }
}
 
// Driver Code
int main()
{
    string S = "aaaaa";
 
    // Function Call
    isAcceptedDFA(S, S.size());
 
    return 0;
}

Java

// Java program for the above approach
class GFG
{
 
// Function to check whether the String
// S satisfy the given DFA or not
static void isAcceptedDFA(String s, int N)
{
    // Stores the count of characters
    int count = 0;
 
    // Iterate over the range [0, N]
    for (int i = 0; i < N; i++) 
    {
 
        // Count and check every
        // element for 'a'
        if (s.charAt(i) == 'a')
            count++;
    }
 
    // If String matches with DFA
    if (count == N && count != 0) 
    {
        System.out.print("Accepted");
    }
 
    // If not matches
    else
    {
        System.out.print("Not Accepted");
    }
}
 
// Driver Code
public static void main(String[] args)
{
    String S = "aaaaa";
 
    // Function Call
    isAcceptedDFA(S, S.length());
}
}
 
// This code is contributed by 29AjayKumar

Python3

# Python3 program for the above approach
 
# Function to check whether the string
# S satisfy the given DFA or not
def isAcceptedDFA(s, N):
   
    # Stores the count of characters
    count = 0
 
    # Iterate over the range [0, N]
    for i in range(N):
 
        # Count and check every
        # element for 'a'
        if (s[i] == 'a'):
            count += 1
 
    # If string matches with DFA
    if (count == N and count != 0):
        print ("Accepted")
 
    # If not matches
    else :
        print ("Not Accepted")
 
# Driver Code
if __name__ == '__main__':
    S = "aaaaa"
 
    # Function Call
    isAcceptedDFA(S, len(S))
 
# This code is contributed by mohit kumar 29

C#

// C# program for the above approach
using System;
class GFG
{
 
// Function to check whether the String
// S satisfy the given DFA or not
static void isAcceptedDFA(String s, int N)
{
   
    // Stores the count of characters
    int count = 0;
 
    // Iterate over the range [0, N]
    for (int i = 0; i < N; i++) 
    {
 
        // Count and check every
        // element for 'a'
        if (s[i] == 'a')
            count++;
    }
 
    // If String matches with DFA
    if (count == N && count != 0) 
    {
        Console.Write("Accepted");
    }
 
    // If not matches
    else
    {
        Console.Write("Not Accepted");
    }
}
 
// Driver Code
public static void Main(String[] args)
{
    String S = "aaaaa";
 
    // Function Call
    isAcceptedDFA(S, S.Length);
}
}
 
// This code is contributed by 29AjayKumar

Javascript

<script>
 
      // JavaScript program for the above approach
      // Function to check whether the String
      // S satisfy the given DFA or not
      function isAcceptedDFA(s, N) {
        // Stores the count of characters
        var count = 0;
 
        // Iterate over the range [0, N]
        for (var i = 0; i < N; i++) {
          // Count and check every
          // element for 'a'
          if (s[i] === "a") count++;
        }
 
        // If String matches with DFA
        if (count === N && count !== 0) {
          document.write("Accepted");
        }
 
        // If not matches
        else {
          document.write("Not Accepted");
        }
      }
 
      // Driver Code
      var S = "aaaaa";
 
      // Function Call
      isAcceptedDFA(S, S.length);
       
</script>

Output:

Accepted

Time Complexity: O(N)
Auxiliary Space: O(1)

Construct a DFA which accept the language L = {aⁿb^m | n > =1, (m) mod 3 = 1}

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Practice Tags :

Strings

Program to construct a DFA which accepts the language L = {aN | N ≥ 1}

C++

Java

Python3

C#

Javascript

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