**Examples of DFA**

By Making sure that you have already cover the topic of DFA. Now let see some examples of DFA in TOC.

**Example 1:**

Design a DFA with ∑ = {0, 1} accepts the only input a string “10”.

**Solution:**

In above example, the language contains only one string because it is specific in question

L= {10}

DFA for above language is given below

**Example:2**

Construct a DFA with ∑ = {a, b} accepts the only input “aaab”.

**Solution:**

The language from given grammar is given below

L= {aaab}

DFA for above language is given below

**Example:3**

Construct a DFA with sigma **∑ = {0, 1},** accepts those string which **starts with 1 and ends with 0.**

**Solution:**

Language for given question is given below

**L= {10, 1100,1010, 1110, 100010, 1000101110….}**

Let draw the DFA which accept all the strings of above language

Note: above automata machine does not accept those strings which are start and end with same input as “10001”

**Example:4**

Construct a DFA with sigma **∑ = {0, 1},** accepts the set of all strings with three consecutive 0’s.

**Solution:**

Language for given question is given below

**L= {000, 1000,0001, 111000, 10001 ….}**

Let draw the DFA which accept all the strings of above language

**Example:5**

Construct a DFA with sigma **∑ = {a, b},** accepts those strings which **has even number of “a” and even number of “b”.**

**Solution:**

Language for given question is given below

**L= {** **ε**, aa, bb, abab, baab, **aabb, aaaabbbb, bbbbaaaa, bbbbbbaaaaaa, ….}**

**Note**: Epsilon (**ε**) represent zero which is even.

Let draw the DFA which accept all the strings of above language

**In Above DFA,**

- If state q1 becomes final instead of q0 then DFA will accept all those strings which have Odd “a” and even “b”.
- And if state q2 becomes final instead of q0 then DFA will accept all those strings which have even “a” and odd “b”.
- And If state q3 becomes final instead of q0 then DFA will accept all those strings which have odd “a” and odd “b”.

As given in following diagram