PROGRAM 7:

Write program to find ε – closure of all states of any given NFA with ε transition.



ALGORITHM:
1. Enter the NFA with ε transition
2. Find the states that can be traversed using for ε transition from the starting state and add it into ε          closure of the starting state.
3. Check for ε transition  in each new state found in step 2, if so add all those states into ε closure of         the starting state.
4. Do repeat Step 2 and Step 3 for each state present in transition table.
5. Display the ε closure of each state in NFA.

PROGRAM:


#include<stdio.h>
#include<conio.h>
struct node
{
int st;
struct node *link;
};
void findclosure(int,int);
void insert_trantbl(int ,char, int);
int findalpha(char);
void findfinalstate(void);
void unionclosure(int);
void print_e_closure(int);
static int set[20],nostate,noalpha,s,notransition,nofinal,start,finalstate[20],c,r,buffer[20];
char alphabet[20];
static int e_closure[20][20]={0};
struct node * transition[20][20]={NULL};
void main()
{
int i,j,k,m,t,n;
struct node *temp;
clrscr();
printf(“enter the number of alphabets?\n”);
scanf(“%d”,&noalpha);
getchar();
printf(“NOTE:- [ use letter e as epsilon]\n”);
printf(“NOTE:- [e must be last character ,if it is present]\n”);
printf(“\nEnter alphabets?\n”);
for(i=0;i<noalpha;i++)
{
alphabet[i]=getchar();
getchar();
}
printf(“Enter the number of states?\n”);
scanf(“%d”,&nostate);
printf(“Enter the start state?\n”);
scanf(“%d”,&start);
printf(“Enter the number of final states?\n”);
scanf(“%d”,&nofinal);
printf(“Enter the final states?\n”);
for(i=0;i<nofinal;i++)
scanf(“%d”,&finalstate[i]);
printf(“Enter no of transition?\n”);
scanf(“%d”,&notransition);
printf(“NOTE:- [Transition is in the form–> qno alphabet qno]\n”,notransition);
printf(“NOTE:- [States number must be greater than zero]\n”);
printf(“\nEnter transition?\n”);
for(i=0;i<notransition;i++)
{
scanf(“%d %c%d”,&r,&c,&s);
insert_trantbl(r,c,s);
}
printf(“\n”);
for(i=1;i<=nostate;i++)
{
c=0;
for(j=0;j<20;j++)
{
buffer[j]=0;
e_closure[i][j]=0;
}
findclosure(i,i);
}
printf(“Equivalent NFA without epsilon\n”);
printf(“———————————–\n”);
printf(“start state:”);
print_e_closure(start);
printf(“\nAlphabets:”);
for(i=0;i<noalpha;i++)
printf(“%c “,alphabet[i]);
printf(“\n States :” );
for(i=1;i<=nostate;i++)
print_e_closure(i);
printf(“\nTnransitions are…:\n”);
for(i=1;i<=nostate;i++)
{
for(j=0;j<noalpha-1;j++)
{
for(m=1;m<=nostate;m++)
set[m]=0;
for(k=0;e_closure[i][k]!=0;k++)
{
t=e_closure[i][k];
temp=transition[t][j];
while(temp!=NULL)
{
unionclosure(temp->st);
temp=temp->link;
}
}
printf(“\n”);
print_e_closure(i);
printf(“%c\t”,alphabet[j] );
printf(“{“);
for(n=1;n<=nostate;n++)
{
if(set[n]!=0)
printf(“q%d,”,n);
}
printf(“}”);
}
}
printf(“\n Final states:”);
findfinalstate();
getch();
}
void findclosure(int x,int sta)
{
struct node *temp;
int i;
if(buffer[x])
return;
e_closure[sta][c++]=x;
buffer[x]=1;
if(alphabet[noalpha-1]==’e’ && transition[x][noalpha-1]!=NULL)
{
temp=transition[x][noalpha-1];
while(temp!=NULL)
{
findclosure(temp->st,sta);
temp=temp->link;
}
}
}
void insert_trantbl(int r,char c,int s)
{
int j;
struct node *temp;
j=findalpha(c);
if(j==999)
{
printf(“error\n”);
exit(0);
}
temp=(struct node *) malloc(sizeof(struct node));
temp->st=s;
temp->link=transition[r][j];
transition[r][j]=temp;
}
int findalpha(char c)
{
int i;
for(i=0;i<noalpha;i++)
if(alphabet[i]==c)
return i;
return(999);
}
void unionclosure(int i)
{
int j=0,k;
while(e_closure[i][j]!=0)
{
k=e_closure[i][j];
set[k]=1;
j++;
}
}
void findfinalstate()
{
int i,j,k,t;
for(i=0;i<nofinal;i++)
{
for(j=1;j<=nostate;j++)
{
for(k=0;e_closure[j][k]!=0;k++)
{
if(e_closure[j][k]==finalstate[i])
{
print_e_closure(j);
}
}
}
}
}
void print_e_closure(int i)
{
int j;
printf(“{“);
for(j=0;e_closure[i][j]!=0;j++)
printf(“q%d,”,e_closure[i][j]);
printf(“}\t”);
}

OUTPUT: