C program for DFA accepting all strings over w ∈(a,b)* containing “aba” as a substring

Problem

Design a DFA for the language L={w1abaw2 | w1,w2 Є(a,b)*}, which means the DFA accepts all strings which contain “aba” as a substring.

Solution

The strings that are accepted by language L= {aba,aabaa, aabab, babab, ababa, …….}

Step 1 − Transition diagram for minimal string (starting string) −

If w1 and w2 are null then the string it generates is “aba” because w1, w2 ε(a,b)*

q0 is the initial state and q3 is the final state.

Step 2 − The final DFA for the given language is as follows −

Explanation

• qo is the initial state q0 on ‘a’ goes to q1 and on ‘b’ goes to q0, according to DFA each state has to generate a transition on both inputs.

• q1 on ‘a’ goes to q1 and on ‘b’ goes to q2, we have to keep in mind according to the given language we need to generate a substring “aba”.

• q2 on ‘a’ goes on q3 on ‘b’ goes to q0 state.

• q3 which is the final state, on input ‘a’ and ‘b’ goes to q3 only.

Transition Table

Let’s see the transition table as follows −

Example

Following is the C program for construction of DFA accepting all strings over w ε(a,b)* which contains “aba” as a substring -

 Live Demo

#include <stdio.h>
#include <string.h>
void checkDFA(char s[] ) {
   // storing initial state
   int initialState = 0;
   //assign initial state to previous state.
   int previousState = initialState;
   int finalState;
   for(int i = 0; i < strlen(s); i++)    {
      if((previousState == 0 && s[i] == 'a') || (previousState == 1 && s[i] == 'a')) {
         finalState = 1;
      }
      if((previousState == 0 && s[i] == 'b') || (previousState == 2 && s[i] == 'b')) {
         finalState = 0;
      }
      if(previousState == 1 && s[i] == 'b') {
         finalState = 2;
      }
      if((previousState == 2 && s[i] == 'a') || (previousState == 3)) {
         finalState = 3;
      }
      previousState = finalState;
   }
   if(finalState == 3) {
      printf("given string is Accepted");
   }
   else
   {
      printf("given string is Not Accepted");
   }
}
int main() {
   // Given string
   char s[40];
   printf("implementation of DFA which having a sub string 'aba':
 enter a string:");
   scanf("%s",s);
   checkDFA(s);
   return 0;
}

Output

The output is as follows −

Run 1:
implementation of DFA which having a sub string 'aba':
enter a string:aba
given string is Accepted.
Run 2:
implementation of DFA which having a sub string 'aba':
enter a string:abba
given string is Not Accepted.