C program to simulate Nondeterministic Finite Automata (NFA)

Background

An NFA is typically described using a directed graph. Each edge and vertex is labeled either 0 or 1 representing possible transitions. Vertices represent the states of the NFA. Those labeled 0 are non­ accepting states, and those labeled 1 are accepting states.

  • It takes an input string of finite length. Typically, the input string is a binary sequence of 0’s and 1’s.
  • We begin with the vertex 1 which is always the start state and follow the edges sequentially given by the bits of input string until the input string has no further bit.
  • The term ‘non ­deterministic’ means that at any state V we have more than one choice of following an edge. The NFA consumes the input string and set of states Q represents the possible moves of NFA.
  • If Q contains at least one state where the last vertex is accepting then we say that the NFA has accepted the input string otherwise the NFA has rejected the input string.

Example of NFA:11



Starting state - vertex 1
Accepting states - Vertices with double circles(label 1) // Vertex 4
Non ­accepting states - single circles (label 0). // Vertices 1, 2 and 3.

How to check for acceptance of a string?

For Input : 1010

  • In state 1, we have two possibilities, either follow the self loop and stay in state 1 or follow the edge labeled 1 and go to state 3.
                            {1} 1010 --> {1, 3} 010
  • In state 3, there is no edge labeled 0, so the computation will die out.
  • In state 1, we have two possibilities, either follow the self loop and stay in state 1, or follow the edge labeled 0 to state 2.
                            {1, 3} 010 --> {1, 2} 10
  • Now there is no edge labeled 1 from state 2. The computation will die out. We have two possibilities: either follow the self loop to state 1 or follow the edge labeled 1 to state 3.
                             {1, 2} 10 --> {1, 3} 0
  • In state 3, there is no edge labeled 0. So the computation will die out. In state 1, we have two possibilities: either follow the self loop to state 1 or the edge labeled 0 to state 2.
                                 {1, 3} 0 --> {1, 2}
  • Now the NFA has consumed the input. It can be either be in states 1 or 2, both of which are non ­accepting. So the NFA has rejected the input 1010.

For Input : 1100

          {1} 1100 --> {1, 3} 100 {1, 3} 100 --> {1, 3, 4} 00 {1, 3, 4} 
                  00--> {1, 2, 4} 0 {1, 2, 4} 0--> {1, 2, 4}
  • Now the NFA has consumed the input. It can either be in state 1, 2 or 4. State 4 is an accepting state. So, the NFA accepts the string 1100.
  • We can easily verify that the given NFA accepts all binary strings with “00” and/or “11” as a substring.

C Program to simulate Nondeterministic Finite Automata (NFA)

Input Format:  The adjacency list representation of the NFA is in the following format.

The given example will be represented as

Total Number of Edges: 4

Edge Connectivity:

1 0 4 0 1 0 2 1 1 1 3

2 0 1 0 4



3 0 1 1 4

4 1 2 0 4 1 4

Output Format:  The first 10 binary strings which are accepted by the NFA  in lexicographical order (e denotes the empty string): {e, 0, 1, 00, 01, 10, 11, 000, …}

The sample output for the given test case is as follows:

00

11

000

001

011

100

110

111

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#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>
  
int row = 0;
  
// A structure to represent an adjacency list node
struct node
{
    int data;
    struct node* next;
    char edgetype;
  
}typedef node;
  
// Adds an edge to an adjacency list
node* push(node* first , char edgetype , int data)
{
    node* new_node = (node*)malloc(sizeof(node));
    new_node->edgetype = edgetype;
    new_node->data = data;
    new_node->next = NULL;
    if (first==NULL)
    {
        first = new_node;
        return new_node;
    }
    first->next = push(first->next,edgetype,data);
    return first;
}
  
//Recursive function to check acceptance of input
int nfa(node** graph, int current, char* input,
        int* accept, int start)
{
    if (start==(int)strlen(input))
        return accept[current];
  
    node* temp = graph[current];
    while (temp != NULL)
    {
      if (input[start]==temp->edgetype)
        if (nfa(graph,temp->data,input,accept,start+1==1)
           return 1;
      temp=temp->next;
    }
    return 0;
}
  
//Function to generate binary strings of size n
void generate(char** arr, int size, char *a)
{
    if (size==0)
    {
        strcpy(arr[row], a);
        row++;
        return;
    }
    char b0[20] = {'\0'};
    char b1[20] = {'\0'};
    b0[0] = '0';
    b1[0] = '1';
  
    //Recursively generate the binary string
    generate((char**)arr, size-1, strcat(b0,a)); //Add 0 in front
    generate((char**)arr, size-1, strcat(b1,a)); //Add 1 in front
    return;
  
}
  
// Driver program to test above functions
int main()
{
    int n;
    int i, j;
    scanf("%d", &n); //Number of nodes
    node* graph[n+1]; //Create a graph
  
    for (i=0;i<n+1;i++)
        graph[i]=NULL;
  
  
    int accept[n+1]; //Array to store state of vertex
  
    for (i=0; i<n; i++)
    {
        //Index of vertex , Acceptance state , Number of edges
        int index,acc,number_nodes;
        scanf("%d%d%d",&index,&acc,&number_nodes);
        accept[index]=acc; //Store acceptance
  
        for (j=0;j<number_nodes;j++) //Add all edges
        {
            int node_add;
            int edge;
            scanf("%d%d",&edge,&node_add);
            graph[index] = push(graph[index],'0'+edge,node_add);
        }
    }
  
    int size = 1; //Size of input
    int count = 0; //Keep count of output strings
  
    if (accept[1]==1) //Check for empty string
    {
        printf("e\n");
        count++;
    }
  
    while (count < 11)
    {
        char** arr;
        int power = pow(2,size);
        arr = (char**)malloc(power*sizeof(char*));
  
        for (i=0;i<power;i++)
            arr[i] = (char*)malloc(size*sizeof(char));
  
        char a[20] = {'\0'};
  
        generate((char**)arr,size,a); //Generate inputs
  
        for (i=0; i<power; i++)
        {
            char input[20] = {'\0'};
  
            for (j=0; j<size; j++)
            {
                char foo[2];
                foo[0] = arr[i][size-1-j];
                foo[1] = '\0';
                strcat(input,foo);
                                //Copy generated string input
            }
  
            int result = nfa(graph,1,input,accept,0);
                        // Store result of nfa
  
            if (result==1)
            {
                printf("%s\n",input);
                                // Print if accepted
                count++;
            }
  
            if (count==10)
                return 0;
        }
  
        size++; //Increment size of binary string input
        row=0;
    }
  
    return 0;
}

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Input:

4
1 0 4 0 1 0 2 1 1 1 3
2 0 1 0 4
3 0 1 1 4
4 1 2 0 4 1 4

Output:

00
11
000
001
011
100
110
111
0000
0001

This article is contributed by Arjun Moolrajani. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above




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