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📜  DFA接受w∈(a,b)*上的所有字符串,其中包含“ aba”作为子字符串

📅  最后修改于: 2021-08-24 05:06:14             🧑  作者: Mango

给定一个二进制字符串S,任务是为DFA Machine写一个程序,该程序接受w∈(a,b) *上包含“ aba”作为子字符串的所有所有字符串的集合。

例子 :

Input-1 : ababa
Output : Accepted
Explanation : "ababa" consists "aba"

Input-2 : abbbb
Output : Not accepted
Explanation : "ababa" does not consist "aba"

方法:以下是针对给定问题设计的DFA计算机。为DFA状态构造一个转换表,并分析每个状态之间的转换。以下是步骤–

所需语言:

L = {aba, baba, abab, aababbb.....}

解释 :

  1. 首先,将有4个状态。(例如q 0 ,q 1 ,q 2 ,q 3 ) , 和 q 0是初始状态,q 3是最终状态。
  2. 最初我们将处于q 0状态,现在我们开始读取给定的字符串。
  • 当我们读“ b”时,我们将保持相同的状态
  • 如果我们读“ a”,那么它将转换为状态q 1

3.假设现在我们处于q 1状态。

  • 当我们读“ a”时,我们将保持相同的状态。
  • 如果我们读“ b”,我们将过渡到状态q 2

4.假设现在我们处于q 2状态。

  • 如果我们读“ a”,它将转换为状态q 3
  • 如果我们读取“ b”,它将转换为状态q 0。

5.假设我们处于最终状态(q 3 )

  • 当我们读“ a”或“ b”时,我们保持相同的状态。

6.该DFA接受的所有字符串都将以“ aba”作为其子字符串。转换表:

Current state Final state
a b
q0 q1 q0
q1 q1 q2
q2 q3 q0
q3 q3 q3

以下是上述方法的实施–

C++
// C++ program for the above approach
#include 
#include 
using namespace std;
  
// Function to check whether the given
// string is accepted by DFA or not
void checkValidDFA(string s)
{
    // Stores initial state of DFA
    int initial_state = 0;
    // Stores previous state of DFA
    int previous_state = initial_state;
    // Stores final state of DFA
    int final_state;
    // Iterate through the string
    for (int i = 0; i < s.length(); i++) {
        // Checking for all combinations
        if ((previous_state == 0 && s[i] == 'a') || 
        (previous_state == 1 && s[i] == 'a')) {
            final_state = 1;
        }
        if ((previous_state == 0 && s[i] == 'b') || 
        (previous_state == 2 && s[i] == 'b')) {
            final_state = 0;
        }
        if (previous_state == 1 && s[i] == 'b') {
            final_state = 2;
        }
        if ((previous_state == 2 && s[i] == 'a') || 
        (previous_state == 3)) {
            final_state = 3;
        }
        // Update the previous_state
        previous_state = final_state;
    }
    // If final state is reached
    if (final_state == 3) {
        cout << "Accepted" << endl;
    }
    // Otherwise
    else {
        cout << "Not Accepted" << endl;
    }
}
  
// Driver Code
int main()
{
    // Given string
    string s = "ababa";
    // Function Call
    checkValidDFA(s);
}


C
// C++ program for the above approach 
#include 
#include 
    
// Function to check whether the given 
// string is accepted by DFA or not
void checkValidDFA(char s[] ) 
{
    // Stores initial state of DFA
    int initial_state = 0;
    // Stores previous state of DFA
    int previous_state = initial_state; 
    // Stores final state of DFA 
    int final_state;
    // Iterate through the string 
    for(int i = 0; i < strlen(s); i++)
    {
      // Checking for all combinations     
      if((previous_state == 0 && s[i] == 'a') || 
      (previous_state == 1 && s[i] == 'a'))
      {
          final_state = 1;
      }
      if((previous_state == 0 && s[i] == 'b') || 
      (previous_state == 2 && s[i] == 'b'))
      {
          final_state = 0;
      }
      if(previous_state == 1 && s[i] == 'b')
      {
          final_state = 2;
      }
      if((previous_state == 2 && s[i] == 'a') || 
      (previous_state == 3))
      {
          final_state = 3;
      }
        // Update the previous_state
        previous_state = final_state;
    }
    // If final state is reached
    if(final_state == 3)
    {
        printf("Accepted");
    }
    // Otherwise 
    else
    {
        printf("Not Accepted");
    } 
}
  
// Driver Code
int main()
{
    // Given string
    char s[] = "ababa";
      
    // Function Call 
    checkValidDFA(s);
}


输出 :

Accepted

时间复杂度: O(N)
辅助空间: O(1)

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