Designing Non-Deterministic Finite Automata (Set 3)
Last Updated :
29 Jan, 2024
Prerequisite: Finite Automata IntroductionÂ
In this article, we will see some designing of Non-Deterministic Finite Automata (NFA).
Problem-1: Construction of a minimal NFA accepting a set of strings over {a, b} in which each string of the language starts with ‘ab’.Â
Explanation: The desired language will be like:Â
Â
L1 = {ab, abba, abaa, ...........}
Here as we can see that each string of the above language starts with ‘ab’ and end with any alphabet either ‘a’ or ‘b’.Â
But the below language is not accepted by this NFA because none of the string of below language starts with ‘ab’.Â
Â
L2 = {ba, ba, babaaa..............}
The state transition diagram of the desired language will be like below:Â
Â
In the above NFA, the initial state ‘X’ on getting ‘a’ as the input it transits to a state ‘Y’. The state ‘Y’ on getting ‘b’ as the input it transits to a final state ‘Z’. The final state ‘Z’ on getting either ‘a’ or ‘b’ as the input it remains in the state of itself.Â
Â
Python Implementation:
Â
Python3
def stateX(n):
if ( len (n) = = 0 ):
print ("string not accepted")
else :
if (n[ 0 ] = = 'a' ):
stateY(n[ 1 :])
elif (n[ 0 ] = = 'b' ):
print ("string not accepted")
def stateY(n):
if ( len (n) = = 0 ):
print ("string not accepted")
else :
if (n[ 0 ] = = 'a' ):
print ("string not accepted")
elif (n[ 0 ] = = 'b' ):
stateZ(n[ 1 :])
def stateZ(n):
if ( len (n) = = 0 ):
print ("string accepted")
else :
if (n[ 0 ] = = 'a' ):
stateZ(n[ 1 :])
elif (n[ 0 ] = = 'b' ):
stateZ(n[ 1 :])
n = input ()
stateX(n)
|
Problem-2: Construction of a minimal NFA accepting a set of strings over {a, b} in which each string of the language is not starting with ‘ab’.Â
Explanation: The desired language will be like:Â
Â
L1 = {ba, bba, bbaa, ...........}
Here as we can see that each string of the above language is not starting with ‘ab’ but can end with either ‘a’ or ‘b’.Â
But the below language is not accepted by this NFA because some of the string of below language starts with ‘ab’.Â
Â
L2 = {ab, aba, ababaab..............}
The state transition diagram of the desired language will be like below:Â
Â
In the above NFA, the initial state ‘X’ on getting ‘b’ as the input it transits to a state ‘Y’. The state ‘Y’ on getting either ‘a’ or ‘b’ as the input it transits to a final state ‘Z’. The final state ‘Z’ on getting either ‘a’ or ‘b’ as the input it remains in the state of itself.Â
Â
Python Implementation:
Â
C++
#include <iostream>
#include <string>
void stateX( const std::string& n);
void stateY( const std::string& n);
void stateZ( const std::string& n);
void stateZ( const std::string& n) {
if (n.empty()) {
std::cout << "string accepted" << std::endl;
} else if (n[0] == 'a' ) {
stateZ(n.substr(1));
} else if (n[0] == 'b' ) {
stateZ(n.substr(1));
}
}
void stateY( const std::string& n) {
if (n.empty()) {
std::cout << "string not accepted" << std::endl;
} else if (n[0] == 'a' ) {
std::cout << "string not accepted" << std::endl;
} else if (n[0] == 'b' ) {
stateZ(n.substr(1));
}
}
void stateX( const std::string& n) {
if (n.empty()) {
std::cout << "string not accepted" << std::endl;
} else if (n[0] == 'a' ) {
stateY(n.substr(1));
} else if (n[0] == 'b' ) {
std::cout << "string not accepted" << std::endl;
}
}
int main() {
std::string input = "bba" ;
stateX(input);
return 0;
}
|
Java
import java.util.Scanner;
public class StateMachine {
static void stateZ(String n) {
if (n.isEmpty()) {
System.out.println( "string accepted" );
} else if (n.charAt( 0 ) == 'a' ) {
stateZ(n.substring( 1 ));
} else if (n.charAt( 0 ) == 'b' ) {
stateZ(n.substring( 1 ));
}
}
static void stateY(String n) {
if (n.isEmpty()) {
System.out.println( "string not accepted" );
} else if (n.charAt( 0 ) == 'a' ) {
System.out.println( "string not accepted" );
} else if (n.charAt( 0 ) == 'b' ) {
stateZ(n.substring( 1 ));
}
}
static void stateX(String n) {
if (n.isEmpty()) {
System.out.println( "string not accepted" );
} else if (n.charAt( 0 ) == 'a' ) {
stateY(n.substring( 1 ));
} else if (n.charAt( 0 ) == 'b' ) {
System.out.println( "string not accepted" );
}
}
public static void main(String[] args) {
String input = "bba" ;
stateX(input);
}
}
|
Python3
def stateX(n):
if ( len (n) = = 0 ):
print ("string not accepted")
else :
if (n[ 0 ] = = 'a' ):
print ("string not accepted")
elif (n[ 0 ] = = 'b' ):
stateY(n[ 1 :])
def stateY(n):
if ( len (n) = = 0 ):
print ("string not accepted")
else :
if (n[ 0 ] = = 'a' ):
stateZ(n[ 1 :])
elif (n[ 0 ] = = 'b' ):
stateZ(n[ 1 :])
def stateZ(n):
if ( len (n) = = 0 ):
print ("string accepted")
else :
if (n[ 0 ] = = 'a' ):
stateZ(n[ 1 :])
elif (n[ 0 ] = = 'b' ):
stateZ(n[ 1 :])
n = input ()
stateX(n)
|
Like Article
Suggest improvement
Share your thoughts in the comments
Please Login to comment...