Designing Non-Deterministic Finite Automata (Set 1)
Last Updated :
28 Jan, 2024
Prerequisite:
Finite Automata Introduction
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 ‘a’.
Explanation:
The desired language will be like:
L1 = {ab, abba, abaa, ...........}
Here as we can see that each string of the above language starts with ‘a’ and end with any alphabet either ‘a’ or ‘b’. But the below language is not accepted by this NFA because none of the string of below language starts with ‘a’.
L2 = {ba, ba, babaaa..............}
The state transition diagram of the desired language will be like below:
In the above NFA, the initial state ‘X’ on getting ‘a’ as the input it transits to a final state ‘Y’. The final state ‘Y’ on getting either ‘a’ or ‘b’ as the input it remains in the state of itself.
Python Implementation:
C++
#include <iostream>
#include <string>
void stateX( const std::string& n);
void stateY( const std::string& n);
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;
}
}
}
void stateY( const std::string& n) {
if (n.empty()) {
std::cout << "String accepted" << std::endl;
} else {
if (n[0] == 'a' ) {
stateY(n.substr(1));
}
else if (n[0] == 'b' ) {
stateY(n.substr(1));
}
}
}
int main() {
std::string inputString= "ababa" ;
stateX(inputString);
return 0;
}
|
Java
public class StateMachine {
public 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 stateY(String n) {
if (n.isEmpty()) {
System.out.println( "String accepted" );
} else {
if (n.charAt( 0 ) == 'a' ) {
stateY(n.substring( 1 ));
}
else if (n.charAt( 0 ) == 'b' ) {
stateY(n.substring( 1 ));
}
}
}
public static void main(String[] args) {
String inputString = "ababa" ;
stateX(inputString);
}
}
|
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 accepted")
else :
if (n[ 0 ] = = 'a' ):
stateY(n[ 1 :])
elif (n[ 0 ] = = 'b' ):
stateY(n[ 1 :])
n = input ()
stateX(n)
|
C#
using System;
class StateMachine
{
static void StateX( string n)
{
if ( string .IsNullOrEmpty(n))
{
Console.WriteLine( "String not accepted" );
}
else
{
if (n[0] == 'a' )
{
StateY(n.Substring(1));
}
else if (n[0] == 'b' )
{
Console.WriteLine( "String not accepted" );
}
}
}
static void StateY( string n)
{
if ( string .IsNullOrEmpty(n))
{
Console.WriteLine( "String accepted" );
}
else
{
if (n[0] == 'a' )
{
StateY(n.Substring(1));
}
else if (n[0] == 'b' )
{
StateY(n.Substring(1));
}
}
}
static void Main()
{
string inputString = "ababa" ;
StateX(inputString);
}
}
|
output:
String accepted
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 ‘a’.
Explanation:
The desired language will be like:
L1 = {ba, bba, bbaa, ...........}
Here as we can see that each string of the above language is not starting with ‘a’ but can end with either ‘a’ or ‘b’. But the below language is not accepted by this NFA because some of the string of below language starts with ‘a’.
L2 = {ab, aba, ababaab..............}
The state transition diagram of the desired language will be like below:
In the above NFA, the initial state ‘X’ on getting ‘b’ as the input it transits to a final state ‘Y’. The final state ‘Y’ on getting either ‘a’ or ‘b’ as the input it remains in the state of itself.
Python Implementation:
Python3
def stateX(n):
if ( len (n) = = 0 ):
print ("string not accepted")
else :
if (n[ 0 ] = = 'b' ):
stateY(n[ 1 :])
elif (n[ 0 ] = = 'a' ):
print ("string not accepted")
def stateY(n):
if ( len (n) = = 0 ):
print ("string accepted")
else :
if (n[ 0 ] = = 'a' ):
stateY(n[ 1 :])
elif (n[ 0 ] = = 'b' ):
stateY(n[ 1 :])
n = input ()
stateX(n)
|
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