Examples:which means any no of elements, and = which means any no of elements greater than 1.
Input: a a b b b Output: NOT ACCEPTED // n = 2 (>=1), m=3 ((3) mod3 != 1) Input: a a a b Output: ACCEPTED // n = 3 (>=1), m = 1 ((1) mod 3= 1) Input: b b b b Output: NOT ACCEPTED // n = 0(must be >=1), m = 4 ((4) mod 3 = 1)Approaches:
It’s construction should contain the following steps:
-
Step-1: Construct FA for
means having any number of a’s greater than one. -
Step-2: Construct FA for
means having exactly -
Step-3: Construct FA for
means having b’s equal to multiple of 3 . - Step-4: Concatenate the three FA and make single DFA. Always maintain the order of a, b and c.
-
Given DFA has following states. State 2 leads to the acceptance of the string.Whereas states 0, 1, 3, 4 and 5 leads to the rejection of the string.
DFA State Transition Diagram:
C/C++
// C program to implement DFS that accepts // all string which follow the language // L = { a^n b^m ; n >=1, (m)mod 3=1} #include <stdio.h> #include <string.h> // dfa tells the number associated // string end in which state. int dfa = 0;
// This function is for // the starting state (Q0)of DFA void start(char c)
{ if (c == 'a') {
dfa = 1;
}
else if (c == 'b') {
dfa = 5;
}
// -1 is used to check for any invalid symbol
else {
dfa = -1;
}
} // This function is for the first state (Q1) of DFA void state1(char c)
{ if (c == 'a') {
dfa = 1;
}
else if (c == 'b') {
dfa = 2;
}
else {
dfa = -1;
}
} // This function is for the second state (Q2) of DFA void state2(char c)
{ if (c == 'b') {
dfa = 3;
}
else if (c == 'a') {
dfa = 5;
}
else {
dfa = -1;
}
} // This function is for the third state (Q3)of DFA void state3(char c)
{ if (c == 'b') {
dfa = 4;
}
else if (c == 'a') {
dfa = 5;
}
else {
dfa = -1;
}
} // This function is for the forth state (Q4)of DFA void state4(char c)
{ if (c == 'b') {
dfa = 2;
}
else if (c == 'a') {
dfa = 5;
}
else {
dfa = -1;
}
} // This function is for the fifth state (Q5) of DFA void state5(char c)
{ dfa = -1;
} int isAccepted(char str[])
{ // store length of string
int i, len = strlen(str);
for (i = 0; i < len; i++) {
if (dfa == 0)
start(str[i]);
else if (dfa == 1)
state1(str[i]);
else if (dfa == 2)
state2(str[i]);
else if (dfa == 3)
state3(str[i]);
else if (dfa == 4)
state4(str[i]);
else if (dfa == 5)
state5(str[i]);
else
return 0;
}
if (dfa == 2)
return 1;
else
return 0;
} // driver code int main()
{ char str[] = "aaabbbb";
if (isAccepted(str))
printf("ACCEPTED");
else
printf("NOT ACCEPTED");
return 0;
} // This code is contributed by SHUBHAMSINGH10. |
Java
// Java program to implement DFS that accepts // all string which follow the language // L = { a^n b^m ; n >=1, (m)mod 3=1} import java.util.*;
class GFG {
// dfa tells the number associated // string end in which state. static int dfa = 0;
// This function is for // the starting state (Q0)of DFA static void start(char c)
{ if (c == 'a') {
dfa = 1;
}
else if (c == 'b') {
dfa = 5;
}
// -1 is used to check for any invalid symbol
else {
dfa = -1;
}
} // This function is for the first state (Q1) of DFA static void state1(char c)
{ if (c == 'a') {
dfa = 1;
}
else if (c == 'b') {
dfa = 2;
}
else {
dfa = -1;
}
} // This function is for the second state (Q2) of DFA static void state2(char c)
{ if (c == 'b') {
dfa = 3;
}
else if (c == 'a') {
dfa = 5;
}
else {
dfa = -1;
}
} // This function is for the third state (Q3)of DFA static void state3(char c)
{ if (c == 'b') {
dfa = 4;
}
else if (c == 'a') {
dfa = 5;
}
else {
dfa = -1;
}
} // This function is for the forth state (Q4)of DFA static void state4(char c)
{ if (c == 'b') {
dfa = 2;
}
else if (c == 'a') {
dfa = 5;
}
else {
dfa = -1;
}
} // This function is for the fifth state (Q5) of DFA static void state5(char c)
{ dfa = -1;
} static int isAccepted(char str[])
{ // store length of string
int i, len = str.length;
for (i = 0; i < len; i++) {
if (dfa == 0)
start(str[i]);
else if (dfa == 1)
state1(str[i]);
else if (dfa == 2)
state2(str[i]);
else if (dfa == 3)
state3(str[i]);
else if (dfa == 4)
state4(str[i]);
else if (dfa == 5)
state5(str[i]);
else
return 0;
}
if (dfa == 2)
return 1;
else
return 0;
} // Driver code public static void main(String[] args) {
char str[] = "aaabbbb".toCharArray();
if (isAccepted(str)==1)
System.out.println("ACCEPTED");
else
System.out.println("NOT ACCEPTED");
}
} // This code is contributed by Rajput-Ji |
Python 3
# Python3 program to implement DFS that accepts # all Stringing which follow the language # L = {a ^ n b ^ m | n >= 1, (m)mod 3 = 1 } # This function is for the dfa = starting # dfa = state (zeroth) of DFA def start(c):
if (c == 'a'):
dfa = 1
elif (c == 'b'):
dfa = 5
# -1 is used to check for any
# invalid symbol
else:
dfa = -1
return dfa
# This function is for the first # dfa = state of DFA def state1(c):
if (c == 'a'):
dfa = 1
elif (c == 'b'):
dfa = 2
else:
dfa = -1
return dfa
# This function is for the second # dfa = state of DFA def state2(c):
if (c == 'b'):
dfa = 3
elif (c == 'a'):
dfa = 5
else:
dfa = -1
return dfa
# This function is for the third # dfa = state of DFA def state3(c):
if (c == 'b'):
dfa = 4
elif (c == 'a'):
dfa = 5
else:
dfa = -1
return dfa
# This function is for the fouth # dfa = state of DFA def state4(c):
if (c == 'b'):
dfa = 2
elif (c == 'a'):
dfa = 5
else:
dfa = -1
return dfa
# This function is for the fifth # dfa = state of DFA def state5(c):
dfa = -1
return dfa
def isAccepted(String):
# store length of Stringing
l = len(String)
# dfa tells the number associated
# with the present dfa = state
dfa = 0
for i in range(l):
if (dfa == 0):
dfa = start(String[i])
elif (dfa == 1):
dfa = state1(String[i])
elif (dfa == 2) :
dfa = state2(String[i])
elif (dfa == 3) :
dfa = state3(String[i])
elif (dfa == 4) :
dfa = state4(String[i])
elif (dfa == 5) :
dfa = state5(String[i])
else:
return 0
if(dfa == 2) :
return 1
else:
return 0
# Driver code if __name__ == "__main__" :
String = "aaabbbb"
if (isAccepted(String)) :
print("ACCEPTED")
else:
print("NOT ACCEPTED")
# This code is contributed by SHUBHAMSINGH10. |
C#
// C# program to implement DFS that accepts // all string which follow the language // L = { a^n b^m ; n >=1, (m)mod 3=1} using System;
public class GFG {
// dfa tells the number associated // string end in which state. static int dfa = 0;
// This function is for // the starting state (Q0)of DFA static void start(char c)
{ if (c == 'a') {
dfa = 1;
}
else if (c == 'b') {
dfa = 5;
}
// -1 is used to check for any invalid symbol
else {
dfa = -1;
}
} // This function is for the first state (Q1) of DFA static void state1(char c)
{ if (c == 'a') {
dfa = 1;
}
else if (c == 'b') {
dfa = 2;
}
else {
dfa = -1;
}
} // This function is for the second state (Q2) of DFA static void state2(char c)
{ if (c == 'b') {
dfa = 3;
}
else if (c == 'a') {
dfa = 5;
}
else {
dfa = -1;
}
} // This function is for the third state (Q3)of DFA static void state3(char c)
{ if (c == 'b') {
dfa = 4;
}
else if (c == 'a') {
dfa = 5;
}
else {
dfa = -1;
}
} // This function is for the forth state (Q4)of DFA static void state4(char c)
{ if (c == 'b') {
dfa = 2;
}
else if (c == 'a') {
dfa = 5;
}
else {
dfa = -1;
}
} // This function is for the fifth state (Q5) of DFA static void state5(char c)
{ dfa = -1;
} static int isAccepted(char []str)
{ // store length of string
int i, len = str.Length;
for (i = 0; i < len; i++) {
if (dfa == 0)
start(str[i]);
else if (dfa == 1)
state1(str[i]);
else if (dfa == 2)
state2(str[i]);
else if (dfa == 3)
state3(str[i]);
else if (dfa == 4)
state4(str[i]);
else if (dfa == 5)
state5(str[i]);
else
return 0;
}
if (dfa == 2)
return 1;
else
return 0;
} // Driver code public static void Main(String[] args) {
char []str = "aaabbbb".ToCharArray();
if (isAccepted(str)==1)
Console.WriteLine("ACCEPTED");
else
Console.WriteLine("NOT ACCEPTED");
}
} // This code has been contributed by 29AjayKumar |
ACCEPTED
Article Tags :
Recommended Articles