Diseñe un autómata finito determinista (DFA) para aceptar el lenguaje L = 
Para crear DFA para el lenguaje, L = { a^nb^m ; n+m=par } usa las matemáticas elementales, que dicen
: par + par = par e impar + impar = par
Ejemplos:
Input: a a b b // n = 2, m = 2, 2 + 2 = 4 (even) Output: ACCEPTED Input: a a a b b b b // n = 3, m = 4, 3 + 4 = 7 (odd) Output: NOT ACCEPTED Input: a a a b b b // n = 3, m = 3, 3 + 3 = 6 (even) Output: ACCEPTED
Enfoques:
hay 2 casos que dan como resultado la aceptación de la string:
- Si tanto n como m son pares entonces su suma será par
- Si tanto n como m son impares, su suma será par
Descripción:
Dado DFA tiene 2 partes. La primera parte consta de los estados 0, 1, 5 y 6, que es tanto para n como para m impar. La segunda parte consta de los estados 2, 3 y 4, tanto para n como para m, es par.
Diagrama de transición de estado de DFA:
Veamos el código de la demostración:
C++
// C++ program to implement DFA that accepts
// all strings which follow the language
// L = { a^n b^m ; n+m=even }
#include <bits/stdc++.h>
using namespace std;
// dfa tells the number associated
// with the present state
int dfa = 0;
// This function is for
// the starting state (zeroth) of DFA
void start(char c)
{
if (c == 'a')
dfa = 1;
else if (c == 'b')
dfa = 2;
// -1 is used to check for any invalid symbol
else
dfa = -1;
}
// This function is for the first state of DFA
void state1(char c)
{
if (c == 'a')
dfa = 0;
else if (c == 'b')
dfa = 5;
else
dfa = -1;
}
// This function is for the second state of DFA
void state2(char c)
{
if (c == 'b')
dfa = 3;
else
dfa = -1;
}
// This function is for the third state of DFA
void state3(char c)
{
if (c == 'b')
dfa = 4;
else
dfa = -1;
}
// This function is for the fourth state of DFA
void state4(char c)
{
if (c == 'b')
dfa = 3;
else
dfa = -1;
}
// This function is for the fifth state of DFA
void state5(char c)
{
if (c == 'b')
dfa = 6;
else
dfa = -1;
}
// This function is for the sixth state of DFA
void state6(char c)
{
if (c == 'b')
dfa = 5;
else
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 if (dfa == 6)
state6(str[i]);
else
return 0;
}
if (dfa == 3 || dfa == 5)
return 1;
else
return 0;
}
// Driver code
int main()
{
char str[] = "aaabbb";
if (isAccepted(str))
cout << "\nACCEPTED\n";
else
cout << "NOT ACCEPTED\n";
return 0;
}
// This code is contributed by SHUBHAMSINGH10
C
// C program to implement DFA that accepts
// all strings which follow the language
// L = { a^n b^m ; n+m=even }
#include <stdio.h>
#include <string.h>
// dfa tells the number associated
// with the present state
int dfa = 0;
// This function is for
// the starting state (zeroth) of DFA
void start(char c)
{
if (c == 'a')
dfa = 1;
else if (c == 'b')
dfa = 2;
// -1 is used to check for any invalid symbol
else
dfa = -1;
}
// This function is for the first state of DFA
void state1(char c)
{
if (c == 'a')
dfa = 0;
else if (c == 'b')
dfa = 5;
else
dfa = -1;
}
// This function is for the second state of DFA
void state2(char c)
{
if (c == 'b')
dfa = 3;
else
dfa = -1;
}
// This function is for the third state of DFA
void state3(char c)
{
if (c == 'b')
dfa = 4;
else
dfa = -1;
}
// This function is for the fourth state of DFA
void state4(char c)
{
if (c == 'b')
dfa = 3;
else
dfa = -1;
}
// This function is for the fifth state of DFA
void state5(char c)
{
if (c == 'b')
dfa = 6;
else
dfa = -1;
}
// This function is for the sixth state of DFA
void state6(char c)
{
if (c == 'b')
dfa = 5;
else
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 if (dfa == 6)
state6(str[i]);
else
return 0;
}
if (dfa == 3 || dfa == 5)
return 1;
else
return 0;
}
// driver code
int main()
{
char str[] = "aaabbb";
if (isAccepted(str))
printf("\nACCEPTED\n");
else
printf("NOT ACCEPTED\n");
return 0;
}
Java
// Java program to implement DFA that accepts
// all strings which follow the language
// L = { a^n b^m ; n+m=even }
class GFG {
// dfa tells the number associated
// with the present 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 = 2;
}
// -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 = 0;
}
else if (c == 'b') {
dfa = 5;
}
else {
dfa = -1;
}
}
// This function is for the
// second state (Q2) of DFA
static void state2(char c)
{
if (c == 'b') {
dfa = 3;
}
else {
dfa = -1;
}
}
// This function is for the
// third state (Q3)of DFA
static void state3(char c)
{
if (c == 'b') {
dfa = 4;
}
else {
dfa = -1;
}
}
// This function is for the
// fourth state (Q4) of DFA
static void state4(char c)
{
if (c == 'b') {
dfa = 3;
}
else {
dfa = -1;
}
}
// This function is for the
// fifth state (Q5) of DFA
static void state5(char c)
{
if (c == 'b') {
dfa = 6;
}
else {
dfa = -1;
}
}
// This function is for the
// sixth state (Q6) of DFA
static void state6(char c)
{
if (c == 'b') {
dfa = 5;
}
else {
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 if (dfa == 6)
state6(str[i]);
else
return 0;
}
if (dfa == 3 || dfa == 5)
return 1;
else
return 0;
}
// Driver code
public static void main(String[] args)
{
char str[] = "aaabbb".toCharArray();
if (isAccepted(str) == 1)
System.out.println("ACCEPTED");
else
System.out.println("NOT ACCEPTED");
}
}
Python3
# Python3 program to implement DFA that accepts
# all strings which follow the language
# L = a ^ n b ^ m n + m = even
# This function is for the dfa = starting
# dfa = state (zeroth) of DFA
def start(c):
if (c == 'a'):
dfa = 1
elif (c == 'b'):
dfa = 2
# -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 = 0
elif (c == 'b'):
dfa = 5
else:
dfa = -1
return dfa
# This function is for the second
# dfa = state of DFA
def state2(c):
if (c == 'b'):
dfa = 3
else:
dfa = -1
return dfa
# This function is for the third
# dfa = state of DFA
def state3(c):
if (c == 'b'):
dfa = 4
else:
dfa = -1
return dfa
# This function is for the fourth
# dfa = state of DFA
def state4(c):
if (c == 'b'):
dfa = 3
else:
dfa = -1
return dfa
# This function is for the fifth
# dfa = state of DFA
def state5(c):
if (c == 'b'):
dfa = 6
else:
dfa = -1
return dfa
# This function is for the sixth
# dfa = state of DFA
def state6(c):
if (c == 'b'):
dfa = 5
else:
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])
elif (dfa == 6):
dfa = state6(String[i])
else:
return 0
if(dfa == 3 or dfa == 5) :
return 1
else:
return 0
# Driver code
if __name__ == "__main__" :
String = "aaabbb"
if (isAccepted(String)) :
print("ACCEPTED")
else:
print("NOT ACCEPTED")
# This code is contributed by
# Shubham Singh(SHUBHAMSINGH10)
C#
// C# program to implement DFA that accepts
// all strings which follow the language
// L = { a^n b^m ; n+m=even }
using System;
class GFG
{
// dfa tells the number associated
// with the present 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 = 2;
}
// -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 = 0;
}
else if (c == 'b')
{
dfa = 5;
}
else
{
dfa = -1;
}
}
// This function is for the
// second state (Q2) of DFA
static void state2(char c)
{
if (c == 'b')
{
dfa = 3;
}
else
{
dfa = -1;
}
}
// This function is for the
// third state (Q3)of DFA
static void state3(char c)
{
if (c == 'b')
{
dfa = 4;
}
else
{
dfa = -1;
}
}
// This function is for the
// fourth state (Q4) of DFA
static void state4(char c)
{
if (c == 'b')
{
dfa = 3;
}
else
{
dfa = -1;
}
}
// This function is for the
// fifth state (Q5) of DFA
static void state5(char c)
{
if (c == 'b')
{
dfa = 6;
}
else
{
dfa = -1;
}
}
// This function is for the
// sixth state (Q6) of DFA
static void state6(char c)
{
if (c == 'b')
{
dfa = 5;
}
else
{
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 if (dfa == 6)
state6(str[i]);
else
return 0;
}
if (dfa == 3 || dfa == 5)
return 1;
else
return 0;
}
// Driver code
public static void Main(String[] args)
{
char []str = "aaabbb".ToCharArray();
if (isAccepted(str) == 1)
Console.WriteLine("ACCEPTED");
else
Console.WriteLine("NOT ACCEPTED");
}
}
/* This code contributed by PrinciRaj1992 */
PHP
<?php
// PHP program to implement DFA that accepts
// all strings which follow the language
// L = { a^n b^m ; n+m=even }
// This function is for the
// starting state (zeroth) of DFA
function start($c, &$dfa)
{
if ($c == 'a') $dfa = 1;
elseif ($c == 'b') $dfa = 2;
// -1 is used to check for any
// invalid symbol
else $dfa = -1;
}
// This function is for the first
// state of DFA
function state1($c, &$dfa)
{
if ($c == 'a') $dfa = 0;
elseif ($c == 'b') $dfa = 5;
else $dfa = -1;
}
// This function is for the second
// state of DFA
function state2($c, &$dfa)
{
if ($c == 'b') $dfa = 3;
else $dfa = -1;
}
// This function is for the third
// state of DFA
function state3($c, &$dfa)
{
if ($c == 'b') $dfa = 4;
else $dfa = -1;
}
// This function is for the fourth
// state of DFA
function state4($c, &$dfa)
{
if ($c == 'b') $dfa = 3;
else $dfa = -1;
}
// This function is for the fifth
// state of DFA
function state5($c, &$dfa)
{
if ($c == 'b') $dfa = 6;
else $dfa = -1;
}
// This function is for the sixth
// state of DFA
function state6($c, &$dfa)
{
if ($c == 'b') $dfa = 5;
else $dfa = -1;
}
function isAccepted($str, &$dfa)
{
// store length of string
$i = 0; $len = sizeof($str);
for ($i = 0; $i < $len; $i++)
{
if ($dfa == 0)
start($str[$i], $dfa);
elseif ($dfa == 1)
state1($str[$i], $dfa);
elseif ($dfa == 2)
state2($str[$i], $dfa);
elseif ($dfa == 3)
state3($str[$i], $dfa);
elseif ($dfa == 4)
state4($str[$i], $dfa);
elseif ($dfa == 5)
state5($str[$i], $dfa);
elseif ($dfa == 6)
state6($str[$i], $dfa);
else
return 0;
}
if($dfa == 3 || $dfa == 5)
return 1;
else
return 0;
}
// Driver code
// dfa tells the number associated
// with the present state
$dfa = 0;
$str = array("a", "a", "a", "b", "b", "b");
if (isAccepted($str, $dfa) != 0)
echo "ACCEPTED";
else
echo "NOT ACCEPTED";
// This code is contributed by
// Adesh kumar Singh(adeshsingh1)
?>
Javascript
<script>
// Javascript program to implement DFA that accepts
// all strings which follow the language
// L = { a^n b^m ; n+m=even }
// dfa tells the number associated
// with the present state
var dfa = 0;
// This function is for
// the starting state (zeroth) of DFA
function start(c)
{
if (c == 'a')
dfa = 1;
else if (c == 'b')
dfa = 2;
// -1 is used to check for any invalid symbol
else
dfa = -1;
}
// This function is for the first state of DFA
function state1(c)
{
if (c == 'a')
dfa = 0;
else if (c == 'b')
dfa = 5;
else
dfa = -1;
}
// This function is for the second state of DFA
function state2(c)
{
if (c == 'b')
dfa = 3;
else
dfa = -1;
}
// This function is for the third state of DFA
function state3(c)
{
if (c == 'b')
dfa = 4;
else
dfa = -1;
}
// This function is for the fourth state of DFA
function state4(c)
{
if (c == 'b')
dfa = 3;
else
dfa = -1;
}
// This function is for the fifth state of DFA
function state5(c)
{
if (c == 'b')
dfa = 6;
else
dfa = -1;
}
// This function is for the sixth state of DFA
function state6(c)
{
if (c == 'b')
dfa = 5;
else
dfa = -1;
}
function isAccepted(str)
{
// Store length of string
var 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 if (dfa == 6)
state6(str[i]);
else
return 0;
}
if (dfa == 3 || dfa == 5)
return 1;
else
return 0;
}
// Driver code
var str = "aaabbb";
if (isAccepted(str))
document.write( "ACCEPTED");
else
document.write( "NOT ACCEPTED");
</script>
Producción:
ACCEPTED
Hay un DFA mínimo para el mismo problema.
Publicación traducida automáticamente
Artículo escrito por RishabhMalik y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA