Examples of NFA
Example 1:
Design a NFA for the transition table as given below:
| Present State | 0 | 1 |
|---|---|---|
| →q0 | q0, q1 | q0, q2 |
| q1 | q3 | ε |
| q2 | q2, q3 | q3 |
| →q3 | q3 | q3 |
Solution:
The transition diagram can be drawn by using the mapping function as given in the table.
Here,
Example 2:
Design an NFA with ∑ = {0, 1} accepts all string ending with 01.
Solution:
Hence, NFA would be:
Example 3:
Design an NFA with ∑ = {0, 1} in which double ‘1’ is followed by double ‘0’.
Solution:
The FA with double 1 is as follows:
It should be immediately followed by double 0.
Then,
Now before double 1, there can be any string of 0 and 1. Similarly, after double 0, there can be any string of 0 and 1.
Hence the NFA becomes:
Now considering the string 01100011
Example 4:
Design an NFA in which all the string contain a substring 1110.
Solution:
The language consists of all the string containing substring 1010. The partial transition diagram can be:
Now as 1010 could be the substring. Hence we will add the inputs 0’s and 1’s so that the substring 1010 of the language can be maintained. Hence the NFA becomes:
Transition table for the above transition diagram can be given below:
| Present State | 0 | 1 |
|---|---|---|
| →q1 | q1 | q1, q2 |
| q2 | q3 | |
| q3 | q4 | |
| q4 | q5 |