📌  相关文章
📜  构建DFA以接受以“ 01”开头或结尾的二进制字符串

📅  最后修改于: 2021-08-27 04:45:46             🧑  作者: Mango

给定二进制字符串str ,任务是构建一个DFA来接受字符串(如果该字符串以“ 01”开头或以“ 01”结尾)。

DFA或确定性有限自动机(DFA)是一种有限状态机,如果达到最终状态则接受字符串(在某些特定条件下),否则将其拒绝。
在DFA中,没有记忆的概念,因此我们必须通过字符来检查字符串的字符,与第0字符开始。问题的输入字符集为{0,1}。为了使DFA有效,必须为每个状态下的输入集的每个符号定义一个转换规则,以转换为有效状态。因此,请按照以下步骤设计DFA:

  • 在这种情况下,以01开头或以01结尾或既以01开头又以01结尾的字符串都是可以接受的。
  • 设置一个初始状态并将其输入字母(即0和1)转换为两个不同的状态。
  • 每次转换后检查字符串是否被接受,以忽略错误。
  • 首先,将DfA设置为最小长度的字符串,然后逐步进行操作。
  • 根据字符串的接受定义最终状态。

逐步设计DFA的方法:

  • 步骤1:将初始状态设为“ A”。可能的最小字符串是01,这是可接受的。为此,从状态“ A”到状态“ B”的转换为0,然后从状态“ B”到状态“ C”的转换为1,并注意该状态“ C”为最终状态。

  • 第2步:现在,我们设计了以01开头的DFA。要接受以01开头的所有字符串,例如011、010、010000、01111、010101000010001等,我们需要将0和1的自循环状态“ C”。此自循环包含0和1的所有组合。

  • 步骤3:现在,我们需要考虑以“ 01”结尾的字符串。我们已经完成了状态“ A”从0到0的转换,然后是状态“ A”的输入1。在以01结尾的最小可能字符串,值为101。为此,将状态“ A”的输入1转换为状态“ D”,然后将输入0的状态从状态“ D”转换为状态“ E”,并且然后执行输入1从状态“ E”到状态“ F”的转换,并注意该“ F”状态为最终状态。

  • 第4步:还有一种可能性,任意数量的1都会以01开始,然后以01结束。为此,请在状态“ D”上进行1的自循环,并且在数量1之前可以有任意数量的零。结尾。为此,将自环设置为0,并将状态设置为“ E”。

  • 步骤5:到目前为止,我们已经处理了以1开头,以01结尾的字符串。现在,我们需要考虑以0开头,以01结尾的字符串。为此,请从状态“ B”表示“ E”。

  • 步骤6:现在我们只剩下状态“ F”的输入字母。从状态“ F”转换输入1到状态“ D”,然后从状态“ F”转换输入0到状态“ E”。

上述DFA的转换表和转换规则:

State Input (0) Input (1)
—>A B D
B E C
C* C C
D E D
E E F
F* E D

下面是上述方法的实现:

C++
// C++ program to check if a string
// either starts or ends with 01
#include
using namespace std;
 
void stateA(string);
void stateB(string);
void stateC(string);
void stateD(string);
void stateE(string);
void stateF(string);
 
// Function for transition
// state A
void checkstateA(string n)
{
     
    // State transition to
    // B if the character is
    // 0
    if(n[0] == '0')
       stateB(n.substr(1));
        
    // State transition to
    // D if the character is
    // 1
    else
       stateD(n.substr(1));
}
 
// Function for transition
// state B        
void stateB(string n)
{
     
    // Check if the string has
    // ended
    if (n.length() == 0)
        cout << "string not accepted";
    else
    {
         
        // State transition to C
        // if the character is 1
        if(n[0] == '1')
            stateC(n.substr(1));
 
        // State transition to D
        // if the character is 0
        else
            stateD(n.substr(1));
    }    
}
 
// Function for transition
// state C
void stateC(string n)
{
    cout << "String accepted";
}
 
// Function for transition
// state D
void stateD(string n)
{
    if (n.length() == 0)
        cout << "string not accepted";
    else
    {
         
        // State transition to D
        // if the character is 1
        if (n[0] == '1')
            stateD(n.substr(1));
 
        // State transition to E
        // if the character is 0
        else
            stateE(n.substr(1));
    }
}
 
// Function for transition
// state E
void stateE(string n)
{
    if (n.length() == 0)
        cout << "string not accepted";
    else
    {
         
        // State transition to E
        // if the character is 0
        if(n[0] == '0')
            stateE(n.substr(1));
 
        // State transition to F
        // if the character is 1
        else
            stateF(n.substr(1));
    }
}
 
// Function for transition
// state F
void stateF(string n)
{
    if(n.length() == 0)
        cout << "string accepred";
    else
    {
         
        // State transition to D
        // if the character is 1
        if(n[0] == '1')
            stateD(n.substr(1));
 
        // State transition to E
        // if the character is 0
        else
            stateE(n.substr(1));
    }
}
 
// Driver code
int main()
{
    string n = "0100101";
     
    checkstateA(n);
    return 0;
}
 
// This code is contributed by chitranayal


Java
// Java program to check if a string
// either starts or ends with 01
import java.util.*;
 
class GFG{
     
// Function for transition
// state A
static void checkstateA(String n)
{
     
    // State transition to
    // B if the character is
    // 0
    if (n.charAt(0) == '0')
       stateB(n.substring(1));
        
    // State transition to
    // D if the character is
    // 1
    else
       stateD(n.substring(1));
}
 
// Function for transition
// state B        
static void stateB(String n)
{
     
    // Check if the string has
    // ended
    if (n.length() == 0)
        System.out.println("string not accepted");
    else
    {
         
        // State transition to C
        // if the character is 1
        if (n.charAt(0) == '1')
            stateC(n.substring(1));
 
        // State transition to D
        // if the character is 0
        else
            stateD(n.substring(1));
    }    
}
 
// Function for transition
// state C
static void stateC(String n)
{
    System.out.println("String accepted");
}
 
// Function for transition
// state D
static void stateD(String n)
{
    if (n.length() == 0)
        System.out.println("string not accepted");
    else
    {
         
        // State transition to D
        // if the character is 1
        if (n.charAt(0) == '1')
            stateD(n.substring(1));
 
        // State transition to E
        // if the character is 0
        else
            stateE(n.substring(1));
    }
}
 
// Function for transition
// state E
static void stateE(String n)
{
    if (n.length() == 0)
       System.out.println("string not accepted");
    else
    {
         
        // State transition to E
        // if the character is 0
        if(n.charAt(0) == '0')
            stateE(n.substring(1));
 
        // State transition to F
        // if the character is 1
        else
            stateF(n.substring(1));
    }
}
 
// Function for transition
// state F
static void stateF(String n)
{
    if (n.length() == 0)
        System.out.println("string accepred");
    else
    {
         
        // State transition to D
        // if the character is 1
        if (n.charAt(0) == '1')
            stateD(n.substring(1));
 
        // State transition to E
        // if the character is 0
        else
            stateE(n.substring(1));
    }
}
 
// Driver Code
public static void main(String args[])
{
    String n = "0100101";
     
    checkstateA(n);
}
}
 
// This code is contributed by jyoti369


Python3
# Python3 program to check if
# a string either starts or
# ends with 01
 
# Function for transition
# state A
def checkstateA(n):
 
    # State transition to
    # B if the character is
    # 0
    if(n[0]=='0'):
        stateB(n[1:])
 
    # State transition to
    # D if the character is
    # 1
    else:
        stateD(n[1:])
 
# Function for transition
# state B        
def stateB(n):
 
    # Check if the string has
    # ended
    if (len(n)== 0):
        print("string not accepted")
    else:   
     
        # State transition to C
        # if the character is 1
        if(n[0]=='1'):
            stateC(n[1:])
 
        # State transition to D
        # if the character is 0
        else:
            stateD(n[1:])
          
# Function for transition
# state C   
def stateC(n):
    print("String accepted")
  
# Function for transition
# state D
def stateD(n):
    if (len(n)== 0):
        print("string not accepted")
    else:   
 
        # State transition to D
        # if the character is 1
        if (n[0]=='1'):
            stateD(n[1:])
 
        # State transition to E
        # if the character is 0
        else:
            stateE(n[1:])
  
# Function for transition
# state E
def stateE(n):
    if (len(n)== 0):
        print("string not accepted")
    else:  
 
        # State transition to E
        # if the character is 0
        if(n[0]=='0'):
            stateE(n[1:])
 
        # State transition to F
        # if the character is 1
        else:
            stateF(n[1:])
  
# Function for transition
# state F
def stateF(n):
    if(len(n)== 0):
        print("string accepred")
    else:
 
        # State transition to D
        # if the character is 1
        if(n[0]=='1'):
            stateD(n[1:])
 
        # State transition to E
        # if the character is 0
        else:
            stateE(n[1:])
      
# Driver code
if __name__ == "__main__":
    n = "0100101"
    checkstateA(n)


C#
// C# program to check if
// a string either starts
// or ends with 01
using System;
using System.Collections;
using System.Collections.Generic;
class GFG{
     
// Function for transition
// state A
static void checkstateA(string n)
{
  // State transition to
  // B if the character is
  // 0
  if(n[0] == '0')
    stateB(n.Substring(1));
 
  // State transition to
  // D if the character is
  // 1
  else
    stateD(n.Substring(1));
}
  
// Function for transition
// state B        
static void stateB(string n)
{    
  // Check if the string has
  // ended
  if (n.Length == 0)
  {
    Console.Write("string not accepted");
  }
  else
  {
    // State transition to C
    // if the character is 1
    if(n[0] == '1')
      stateC(n.Substring(1));
 
    // State transition to D
    // if the character is 0
    else
      stateD(n.Substring(1));
  }    
}
 
// Function for transition
// state C
static void stateC(string n)
{
  Console.Write("string accepted");
}
  
// Function for transition
// state D
static void stateD(string n)
{
  if (n.Length == 0)
    Console.Write("string not accepted");
  else
  {
 
    // State transition to D
    // if the character is 1
    if (n[0] == '1')
      stateD(n.Substring(1));
 
    // State transition to E
    // if the character is 0
    else
      stateE(n.Substring(1));
  }
}
  
// Function for transition
// state E
static void stateE(string n)
{
  if (n.Length == 0)
    Console.Write("string not accepted");
  else
  {
 
    // State transition to E
    // if the character is 0
    if(n[0] == '0')
      stateE(n.Substring(1));
 
    // State transition to F
    // if the character is 1
    else
      stateF(n.Substring(1));
  }
}
  
// Function for transition
// state F
static void stateF(string n)
{
  if(n.Length == 0)
    Console.Write("string accepted");
  else
  {
    // State transition to D
    // if the character is 1
    if(n[0] == '1')
      stateD(n.Substring(1));
 
    // State transition to E
    // if the character is 0
    else
      stateE(n.Substring(1));
  }
}
 
// Driver code
public static void Main(string []args)
{
  string n = "0100101";
  checkstateA(n);
}
}
 
// This code is contributed by rutvik_56


Javascript


输出:
String accepted

如果您希望与行业专家一起参加现场课程,请参阅《 Geeks现场课程》和《 Geeks现场课程美国》。