NFA which accepts set of strings over an alphabet {0, 1, 2} such that the final digit has appeared before
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 :
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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’ occurred before 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 :
C++
#include <bits/stdc++.h>using namespace std;// function of state one or starting statevoid q1(string s, int pos, int len);// function of state twovoid q2(string s, int pos, int len);// function of state threevoid q3(string s, int pos, int len);// function of state fourvoid q4(string s, int pos, int len);// function of state fivevoid q5(string s, int pos, int len);// See diagram for helpvector<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;} |
