NFA which accepts set of strings over an alphabet {0, 1, 2} such that the final digit has appeared before

Last Updated : 14 Jul, 2020

Prerequisite – Introduction of Finite Automata
C++ Program to construct an NFA which accepts the set of strings over an alphabet {0, 1, 2} such that the final digit has appeared before.

Examples :

Input : 01101 
Output : Accepted

Input : 012
Output : Not Accepted

Input : 2
Output : Not Accepted

Input : 0122
Output : Accepted

Explanation:
In the first example, 01101, the last digit ‘1’ occurred at letter number 2 and 3 of the string. Hence it is accepted. In second example, 012, the occurrence of ‘2’ is only at the last place. Hence it is rejected. Similarly with the third example, 2 is rejected. In the last example, the last digit ‘2’ occured befor end of the string hence it is Accepted.

Approach:

Construct a start state.
Construct 3 states for input of 0, 1 and 2.
Repeat the loops in all state for all the inputs.
Connect all the state with a final state.

NFA State Transaction Diagram:

Implementation :

#include <bits/stdc++.h>
using namespace std;
  
// function of state one or starting state
void q1(string s, int pos, int len); 
  
// function of state two
void q2(string s, int pos, int len);
  
// function of state three 
void q3(string s, int pos, int len); 
  
// function of state four
void q4(string s, int pos, int len); 
  
// function of state five
void q5(string s, int pos, int len); 
  
// See diagram for help
  
vector<string> states;
int accepted = 0;
  
// Uncomment this function and the function calls to see
// the path of string from the start state to end state
/*
void printVector()
{
    for (auto i = states.begin(); i != states.end(); i++)
        cout << *i << " ";
    cout << endl;
}
*/
void q5(string s, int pos, int len)
{
    states.push_back("Q5->");
    if (pos == len) {
        // printVector();
        accepted = 1;
    }
    else {
        states.push_back("Dead");
        // printVector();
        states.pop_back();
    }
    states.pop_back();
    return;
}
  
void q4(string s, int pos, int len)
{
    states.push_back("Q4->");
    if (pos == len) {
        // printVector();
        states.pop_back();
        return;
    }
    if (s[pos] == '2')
        q5(s, pos + 1, len);
    q4(s, pos + 1, len);
    states.pop_back();
    return;
}
  
void q3(string s, int pos, int len)
{
    states.push_back("Q3->");
    if (pos == len) {
        // printVector();
        states.pop_back();
        return;
    }
    if (s[pos] == '1')
        q5(s, pos + 1, len);
    q3(s, pos + 1, len);
    states.pop_back();
    return;
}
  
void q2(string s, int pos, int len)
{
    states.push_back("Q2->");
    if (pos == len) {
        // printVector();
        states.pop_back();
        return;
    }
    if (s[pos] == '0')
        q5(s, pos + 1, len);
    q2(s, pos + 1, len);
    states.pop_back();
    return;
}
  
void q1(string s, int pos, int len)
{
    states.push_back("Q1->");
    if (pos == len) {
        // printVector();
        states.pop_back();
        return;
    }
    if (s[pos] == '0')
        q2(s, pos + 1, len);
    else if (s[pos] == '1')
        q3(s, pos + 1, len);
    else if (s[pos] == '2')
        q4(s, pos + 1, len);
  
    q1(s, pos + 1, len);
    states.pop_back();
    return;
}
  
int main()
{
    string s;
    // cin >> s;
    s = "01101";
  
    int pos = 0;
    q1(s, pos, s.length());
  
    if (accepted)
        cout << "Accepted" << endl;
    else
        cout << "Not Accepted" << endl;
    return 0;
}

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